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MEASURING 

THE RESULTS OF 

TEACHING 



BY 



WALTER SCOTT MONROE, Ph.D. 

DIRECTOR OF BUREAU OF COOPERATIVE RESEARCH 
SCHOOL OF EDUCATION, INDIANA UNIVERSITY 




HOUGHTON MIFFLIN COMPANY 

BOSTON NEW YORK CHICAGO 



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COPYRIGHT, 1918, BY WALTER SCOTT MONROE 



ALL RIGHTS RESERVED 



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CAMBRIDGE . MASSACHUSETTS 
U. S. A. 



jaiS -6 1919 
©G. a 5 08 91 ,■ 



EDITOR'S INTRODUCTION 

Up to very recently the quality of instruction given by a 
teacher has been almost entirely a matter of personal opin- 
ion. A teacher was good, average, or poor, largely as he or 
she impressed a principal or supervisor; and the basis for 
estimating these qualities lay largely in the theory as to the 
nature of the educational process possessed by the super- 
visory officer. To a superintendent of the drill and memo- 
rization and martinet type, a creative and stimulative and 
original teacher probably would be classed as poor; whereas 
such a teacher would be highly prized by a superintendent 
in close sympathy with the creative and expressive tenden- 
cies in modern education. Against such personal opinion the 
teacher has had almost no means of defense. On the other 
hand, it has been almost equally difficult for a superin- 
tendent to demonstrate to questioning laymen wherein the 
work of a teacher lacked effectiveness. 

Within recent years a number of personal-estimate scales 
have been devised by students and superintending officers 
for charting, in visual form, the important characteristics 
of teachers. Such charts have been useful in revealing points 
of strength and weakness, both to teachers and to super- 
visory officers. 

Practically within the past five years an entirely new series 
of instruments for estimating teaching efficiency has been 
made available in the form of the new Standardized Tests, 
with their accompanying Standard Scores and Score Charts. 
It is with this new set of measuring tools that this volume 
deals. Much of the early work in evolving and standardizing 
these new measuring scales, and accumulating results from 



vi EDITOR'S INTRODUCTION 

which to work out the Standard Scores, naturally had to be 
quite technical and was hard for the teacher to understand. 
Enough such work has now been done to enable the author 
of this volume to organize and present, in simple and read- 
able form, the essential information needed by grade teachers 
to enable them to use these Standardized Tests to measure 
and determine for themselves the effectiveness of their own 
instruction, what are the points of strength and weakness in 
the work they are doing, and where they should add empha- 
sis and where enough emphasis has been placed. The years 
of important work done by the author in directing the 
teachers of the State of Kansas in estimating and evaluating 
the work of the Kansas schools should in itself insure a 
helpful volume. 

The value of such a book as this one to the teacher in 
service cannot but be large. It is seldom that books of such 
definiteness are written for the use of teachers. A study and 
mastery of the method of this volume mean the acquirement 
of a new tool for estimating personal efficiency and self- 
improvement. The use of the Tests means a new ability to 
diagnose and prescribe. To the work of the teacher in the 
classroom they give a definiteness heretofore unknown. To 
use a military term, they set the " limited objectives" for 
each subject of the course of study, which the teacher is 
expected to reach, but beyond which she is not expected to 
go. They prevent a waste of teaching energy by preventing 
over-emphasis, and set standards in instruction which are 
indisputable because they are based on the school practice 
of the best schools of the United States. By their use teach- 
ers may determine their own efficiency, compare the prog- 
ress of their pupils or class, with pupils or classes elsewhere 
in terms that are definite and measures that are comparable; 
and, if unjustly criticized, they can defend the work they are 
doing. The new Standardized Tests give a definiteness and 



EDITOR'S INTRODUCTION vii 

scientific accuracy to the work of schoolroom instruction 
heretofore unknown, and teachers in all kinds of school sys- 
tems will be benefited by a careful study of this important 
volume. 

Ellwood P. Cubberley 



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PREFACE 

This book is written for the teacher in the elementary 
school. As such it is not intended to be a fundamental 
treatise upon educational measurements, but rather a text 
which will help teachers to use standardized tests to the 
greatest advantage. Only certain ones of the available 
standardized tests are described. This was thought to be 
a more helpful plan than to include all of the available 
tests, because the elementary teacher seldom has at hand 
the information necessary for an intelligent selection of 
standardized tests. The value of a number of the tests 
described in this text has been demonstrated by wide usage. 
Others are just being made available for use. In these cases 
it has been necessary for the author to exercise his judgment 
based upon four years' experience in supplying tests to 
teachers and superintendents through the Bureau of Edu- 
cational Measurements and Standards of the Kansas State 
Normal School, Emporia, Kansas. Some worthy tests have 
been omitted partly because of the limitations of space 
and partly because of other considerations. Other worthy 
tests will doubtless be devised in the future, some of them 
replacing certain of the tests chosen for description in this 
text. 

The feasibility of the test being used by teachers who 
have not had special training in the field of educational meas- 
urements has been kept constantly in mind. Detailed di- 
rections for the use of a test are generally not reproduced, 
for they are furnished with the test when purchased for class 
use. Only those general features which are necessary for 
understanding the tests and the method of handling the 



x PREFACE 

results have been given. It is believed that any teacher who 
studies carefully the descriptions given in this text will have 
no difficulty in using any of the tests described. 

It is the contention of the author that the use of a stand- 
ardized test is justified only when the teacher can use the 
resulting measures as a basis for improving instruction. 
Consequently much space is given to the interpretation of 
scores or measures and the corrective instruction which 
should be given to correct unsatisfactory scores. Unfortu- 
nately little is known about corrective measures for certain 
school subjects. This, however, is a condition which time 
will remedy. 

The author is aware that in a sense he has done little more 
than bring together the results of a number of workers in 
this field and he realizes his indebtedness to them. He 
is particularly indebted to Dean F. J. Kelly and Captain 
J. C. DeVoss who kindly permitted him to use portions of 
their chapters in Educational Tests and Measurements. 

Walter S. Monroe 
Bloomington, Indiana 



CONTENTS 

I. The Inaccuracy of Present School Marks . • 1 
XL TnE Measurement of Ability in Reading ... 22 

III. The Meaning of Scores and Correcting Defects 

in Reading 43 

IV. The Measurement of Ability in the Operations of 
Arithmetic 97 

V. Diagnosis and Corrective Instruction in Arith- 
metic 118 

VI. The Measurement of Ability to solve Problems 
and Corrective Instruction . . . . . . 154 

VII. The Measurement of Ability in Spelling and Cor- 
rective Instruction 175 

VTII. The Measurement of Ability in Handwriting . 203 

IX. The Measurement of Ability in Language and 

Grammar 235 

X. The Measurement of Ability in Geography and 
History 255 

XI. Educational Measurements and the Teacher . 267 

XII. Summary 281 

Appendix 285 

Index 295 



LIST OF FIGURES 

1. Distribution of measures of silent reading ability as meas- 
ured by the Kansas Silent Reading Tests .... 5 

2. Distribution of marks in University of Chicago High 
School in English and History; and distribution of marks 

of two teachers in the same department 7 

3. Distribution of marks assigned to one geometry paper by 
116 teachers 9 

4. Form used in recording the scores obtained by using Mon- 
roe's Standardized Silent Reading Tests .... 28 

5. Forms used in recording the scores obtained by using 
Courtis's Silent Reading Test No. 2 34 

6. Record Sheet for recording scores obtained by using 
Thorndike's Visual Vocabulary Scale 38 

7. A scheme for the graphical representation of the scores 
of Monroe's Standardized Silent Reading Tests; and the 
scores of four seventh-grade pupils 45 

8. Median scores of a school in silent reading as determined 

by the Courtis Silent Reading Test No. 2 . . . .48 

9. A scheme for the graphical representation of scores on 
Gray's Oral Reading Test 50 

10. Scores of a fifth-grade class on Monroe's Standardized 
Silent Reading Tests. Type I 52 

11. Scores of a fourth-grade class on Monroe's Standardized 
Silent Reading Tests. Type II 64 

12. Per cent of 1831 Cleveland pupils found in each on nine 
speed and quality groups in silent reading .... 68 

13. Scores of a fifth-grade class on Monroe's Standardized 
Silent Reading Tests. Type III 70 

14. Silent reading rates of fourth-grade pupils, showing 
effect of corrective treatment 81 

15. Average number of pages of silent reading per pupil dur- 
ing school hours. Supplementary material .... 82 



xiv LIST OF FIGURES 

16. Scores of a 2 A class on the Courtis Silent Reading Test 
No. 2. Type IV 83 

17. Scores of a sixth-grade class on the Courtis Silent Read- 
ing Test No. 2. Type V 85 

18. Improvement in oral-reading rate of twenty -fourth when 
individual and group instruction was used .... 89 

19. Form of tabulation sheet for recording scores obtained by 
using the Courtis Standard Research Tests, Series B, and 
the scores of a seventh-grade class in addition . . . 101 

20. Use of Courtis's Graph Sheet No. 3 110 

21. Type I. The record sheet of a fifth-grade class in addition 120 

22. Type IV. The record sheet of an eighth-grade class in 
multiplication 125 

23. Median scores of two classes in the same city . . .129 

24. Two records of one girl 130 

25. Median scores of three sixth-grade classes .... 132 

26. Individual scores of three sixth-grade pupils in the same 
class. (Class A in Fig. 25) 134 

27. Two records of one pupil on the Cleveland Survey 
Tests 152 

28. Distribution of 91 pupils according to the number of 
words spelled correctly 179 

29. Record sheet for recording pupils' scores on a spelling 
test of fifty words 188 

30. Form of class record sheet for recording scores in hand- 
writing 213 

31. Individual record card, Freeman Scale 216 

32. Standard Score Card for measuring handwriting . . .217 

33. Graphical representation of Ayres's Standards for the 
"Gettysburg Edition" of his Handwriting Scale . 220 

34. Distribution of scores in handwriting of a third-grade 
class 224 

35. Distribution of scores in handwriting of a fourth-grade 
class 230 

36. Distribution of scores in handwriting of a fifth-grade 
class 231 

37. Standard distribution of scores in handwriting . . . 232 



LIST OF FIGURES xv 

38. Class record sheet for use with Willing's Composition 
Scale 242 

39. Record sheet for diagnosis. Charters's Diagnostic Test 

in Language and Grammar 247 

40. Illustrating Courtis's Standard Test in Geography for 
States and important cities of the United States . . . 257 

41. A section of the Hahn-Lackey Geography Scale . 260, 261 

42. Medians in speed and accuracy in addition test for pu- 
pils of grades 4 to 8 inclusive, showing Courtis's medians, 
medians for Cuyahoga County, and for three districts in 

the county 270 

43. Median scores of a sixth-grade class in September, 1917, 
and in April, 1918, as measured by the Courtis Standard 
Research Tests in Arithmetic, Series B 273 

44. Improvement in spelling "efficiency" in certain schools 

of Cleveland, Ohio 275 

45. Effect of continuous use of the Courtis Standard Re- 
search Tests, Series B, in Boston, Eighth Grade, 1915 . 276 




LIST OF TABLES 

1. The rank of problems by teachers' judgments ... 13 

2. Problems ranked according to real difficulty and teach- 
ers' estimates 14 

3. A poor arrangement of scores 27 

4. The same scores rearranged in a better order ... 27 

5. Scores of seven seventh-grade pupils on Monroe's Stand- 
ardized Silent Reading Tests 43 

6. Standard May scores for Monroe's Standardized Silent 
Reading Tests 44 

7. Standard scores for Courtis's Silent Reading Test No. 2 46 

8. The scores of one school 49 

9. Median scores in visual vocabulary (Thorndike Scale A) 49 

10. Standard scores for Gray's Oral Reading Test . . .51 

11. Rate of silent reading in informal testing .... 67 

12. A typical distribution of scores in number of examples 
attempted 103 

13. Three special cases which arise in using Courtis's Stand- 
ard Research Tests, Series B 106 

14. Standard median scores, Courtis's Standard Research 
Tests, Series B 108 

15. The distribution of the pupils of a city according to the 
number of examples attempted, Courtis's Standard Re- 
search Tests, Series B 126 

16. The range of number of examples attempted . . . 127 

17. Frequency of types of errors in subtraction, multiplica- 
tion, and division based upon a study of 812 test papers, 
Courtis's Standard Research Tests, Series B 143 

18. Percentage of failures on vocabulary test in arithmetic 166 

19. Percentage of pupils who failed to draw correctly the fig- 
ures named 167 

20. Median scores for a timed-sentence spelling test of fifty 
words 190 



xviii LIST OF TABLES 

21. The misspelling of eighty seventh-grade pupils on a 
column spelling test 195 

22. Handwriting standards. Rate in letters per minute. 
Quality in terms of Ayres's Scale 219 

23. Median scores for Willing's Composition Scale . . 243 

24. Distributions of differences between two teachers' marks 
on sets of fifth-grade arithmetic papers — first, without 
any effort to unify the methods used, and second, by a 
common standard 279 






MEASURING 
THE KESULTS OF TEACHING 

CHAPTER I 

THE INACCURACY OF PRESENT SCHOOL MARKS 

The measurement of results not new in education. Edu- 
cational measurements are not new in school work, although 
this name has not been applied to them until very recently. 
Since schools have existed, teachers and other school offi- 
cials have attempted to measure the abilities of pupils by 
estimating daily recitations and by examinations. The 
measures of the abilities of pupils obtained in these ways 
are thought to possess a high degree of precision and are 
considered very important. 

The promotion of pupils depends upon the " grades" they 
receive. The ability of a pupil in each of the subjects is 
measured by the teacher's estimate and by examination, 
and if the resulting measures show the pupil to be a few 
points, or in some instances a fraction of a point below the 
"passing mark," the pupil is classified as a failure. If the 
resulting measures equal or are above the "passing mark," 
the pupil is promoted. 

The "grades" or school marks are entered upon the 
monthly or quarterly report cards. Parents, as well as 
teachers and pupils, take these school marks very seriously. 
If Johnnie's "grades" for a given month are below those of 
the preceding months, or, worse still, if they are below those 
of neighbor Smith's Mary, an explanation is demanded. A 



2 MEASURING THE RESULTS OF TEACHING 

permanent record is kept of at least the yearly "grades," 
and the awarding of school honors is based upon it. 

Until recently, practically all admission to college was 
determined jj by examination. Except in the universities 
and colleges of the Central and Western American States, 
the custom still maintains generally throughout the world. 
This practice is based on the assumption that the examining 
committee can determine thereby the effectiveness of the 
candidate's college preparatory work. The civil service, 
from its inception in China centuries ago until the present 
day, has employed the examination as a means for meas- 
uring the ability of persons who desire positions operated 
under this system. 

The use of scientific tests and standards is new. Although 
the measurement of the results of instruction is not new, it 
should be recognized that the use of tests which have been 
scientifically constructed and the interpretation of the re- 
sulting measures by comparison with standards is one of 
the most recent educational developments. Thorndike, " the 
father of this movement," has discovered what is probably 
the earliest record of this new type of educational measure- 
ment. The date of this publication, which was by an English 
schoolmaster, is 1864. In our own country, Rice's report on 
spelling in 1897 marked the beginning of the movement, but 
except for this and a few other pioneer efforts, the develop- 
ment has been confined to the last ten years. Within this 
period those who ridiculed the work of Rice have been 
converted to educational measurements, and standardized 
tests are now generally recognized as one of the most help- 
ful instruments at the command of the teacher and the 
supervisor. 

Recent investigations have shown school marks to be in- 
accurate. One of the most important factors contributing 
to our present use of standardized tests has been a number 



INACCURACY OF SCHOOL MARKS 3 

of investigations made to ascertain the accuracy or reliabil- 
ity of measures obtained by means of teachers' estimates 
and by means of examinations. In the world of physical 
things we measure distance by means of the yardstick, mass 
by means of scales, the volume of liquids by means of gallon 
measures. Measurements of these magnitudes, when made 
carefully with accurate instruments, possess a high degree 
of reliability. By a high degree of reliability we mean, for 
example, that if two persons measure the length of the same 
room by means of the same yardstick or any other yard- 
stick, the two measurements will be approximately equal. 
If they differ by more than one or two inches, we doubt the 
accuracy of both, and we demand that the room be measured 
again. Similarly, in the case of school-children, if we find 
that, when the same children are measured in the same sub- 
jects by two different teachers, the two sets of measures do 
not agree rather closely, we have reason to doubt the accu- 
racy of both sets of measures. On the other hand, if the two 
sets of measures ("grades") agree closely, we have reason 
to believe them accurate or reliable. 

In this chapter we present evidence from three types of 
investigations which show that marks given by teachers 
under ordinary conditions are not accurate measures of the 
abilities of their pupils: (1) Kelly's investigation based upon 
the final "grades" given to pupils in two successive years by 
different teachers; (2) Johnson's investigation based upon 
the distribution of "grades"; (3) the marking of examina- 
tion papers. 

(1) Kelly's investigation. In 1913, Kelly ! made an inves- 
tigation of the marks given to the sixth-grade pupils in four 
ward schools in Hackensack, New Jersey, and the marks 
given to the same pupils when they went to a common 

1 Kelly, F. J., Teachers' Marks. (Teachers College Contributions to 
Education, no. 66, p. 7.) 



4 MEASURING THE RESULTS OF TEACHING 

departmental school for seventh-grade work. This will be 
recognized as a case where the abilities of the same pupils 
were measured by two different sets of teachers, the sixth- 
grade teachers in the ward schools and the seventh-grade 
teachers in the departmental school. Since in the depart- 
mental school all of the pupils were taught arithmetic by 
one teacher, there was an opportunity to compare the 
"grades" given in arithmetic by the sixth-grade teachers in 
the different ward schools. If these teachers were accurate 
in their "grading," we would expect to find that all of the 
pupils who received a mark of "G" (good) in arithmetic in 
the sixth grade would receive approximately the same mark 
in the seventh grade. If, however, the sixth-grade teachers 
were inaccurate in their marking, — that is, some of them 
marked too high or too low, — we would expect to find that 
pupils having the mark of " G" in the sixth grade, but com- 
ing from different schools, would, on the average, receive 
different marks in the seventh grade. This condition was 
found to exist. 

Kelly states his conclusions as follows: 

This means that for work which the teacher in school " C " (one 
of the ward schools) would give a mark of "G" (good) in language, 
penmanship, or history, the teacher in school "D" (another ward 
school) would give less than a mark "F" (fair). 

{2) Johnson's investigation. Another type of investiga- 
tion has been made by Johnson, I Principal of the University 
High School of the University of Chicago. It is based upon 
the fact that when accurate measurements are made of any 
ability of a large group of pupils, the resulting measures are 
distributed; that is, arranged along the scale of measurement, 
in a certain definite way. For example, in Fig. 1 there are* 

1 Johnson, F. W., "A Study of High School Grades"; in School Review, 
vol. 19, pp. 13-24. See also Kelly, F. J., Teachers Marks, p. 11, and follow- 
ing, for reports of similar investigations. 



INACCURACY OF SCHOOL MARKS 5 

represented graphically four distributions of the measures 
of silent reading ability secured by giving the Kansas Silent 
Reading Tests. The number of measures represented in 
each grade is over 5000. The base line of the curve in each 




r . . . ~t 

rttnvi t h ids fa a 



4>* <&**/»» 




im WL> artr-g-^i i* 




mn f ' \^\ w ir Ergs -£ fe r~g ^r 



7* iwwfc. 




M *ljS ^' S g^t 



Fig. 1. Showing the Distribution op Measures of Silent Reading 
Ability as measured by the Kansas Silent Reading Tests. 



case represents the scale of the test, 0, 1, 2, 3, 4, 5, and so on. 
At any point of this base line the height of the broken line 
curve above the base line represents the number of pupils 
having the measure represented. The general shape of these 
four broken line curves is the same. A few pupils received 
very low measures and a few very high ones. The great 



6 MEASURING THE RESULTS OF TEACHING 

majority of the measures are grouped near the middle where 
the curve is highest. A curve which, beginning with the 
low measures, rises gradually and then falls gradually, as do 
those shown in Fig. 1, is called a " normal curve" and rep- 
resents the shape of the distribution when accurate meas- 
urements have been made. If the shape of the curve repre- 
senting the distribution of a particular set of measures dif- 
fers materially from the general shape of the curves in Fig. 1, 
there is reason for questioning the accuracy of the measures. 

In the University High School, "F" denotes failure, and 
the four successive ranks above failure are indicated by 
"D," "C," "B," and "A." For the several departments of 
the school, Johnson tabulated the number of times each 
mark was given during the years 1907-08 and 1908-09. 
The conditions which he found to exist may be illustrated 
by Fig. 2. The upper figure shows the distributions of 
marks in English (left) and history (right) . It will be noted 
that in the case of English a much larger proportion of low 
marks ("F" and "D") were given than in history. For the 
high marks ("A" and "B") just the reverse is true. Both 
curves fail to conform closely to the normal curve described 
above which suggests that the marks may not represent 
accurate measures. 

However, the most striking part of the figure is the lower 
which represents the distributions of the marks of two teach- 
ers in the same department. The distribution for teacher A 
conforms reasonably close to the normal curve, but that for 
teacher B departs from it in a very conspicuous fashion. It 
is obvious that teacher B is accustomed to give "high 
grades." In so doing he has furnished evidence that his 
marks are probably inaccurate. 

(3) Marking examination papers. The written examina- 
tion is the most common means of measuring the abilities 
of pupils, although many teachers and school patrons oppose 






INACCURACY OF SCHOOL MARKS 



its use. They contend that pupils working under pressure 
frequently become nervous and confused and consequently 
cannot do themselves justice, while other pupils, who have 
no real grasp of the subject, are able by cramming to write 



£n*lisK 































History 







Teach 


erA 









Teacher B 



Fig. 2. (Upper.) Showing Distribution Marks in University of Chi- 
cago High School in English and History. (Lower.) Showing Dis- 
tribution of Marks of Two Teachers in the Same Department. 
(After Johnson.) 

excellent papers. It is also contended that the questions are 
frequently not well selected and do not pertain to the essen- 
tials of the subject. 

There is probably some truth in the above assertions, but 
within the past few years there have been a number of in- 
vestigations to ascertain if teachers mark examination 



8 MEASURING THE RESULTS OF TEACHING 

papers accurately, assuming that what appears on the papers 
is a true record of the abilities of the pupils. Starch and 
Elliott l investigated the accuracy with which teachers 
marked papers in English, geometry, and history. Their 
method and the facts revealed may be illustrated by the 
case of geometry. 

A facsimile reproduction was made of an actual examina- 
tion paper in plane geometry. A copy of this reproduction 
was sent to each of the high schools included in the North 
Central Association of Colleges and Secondary Schools, with 
the request that it be marked on the scale of one hundred 
per cent by the teacher of geometry. The teacher was asked 
to mark the paper by the method he was accustomed to use. 
Papers were returned from 116 schools, and the results tab- 
ulated. When we consider that the subject-matter of geom- 
etry is quite definite, and that the papers were marked by 
teachers who were thoroughly acquainted with the subject, 
it would seem that we might expect the marks or "grades" 
placed upon this examination paper to be in close agree- 
ment. However, exactly the opposite was the case. 

Distribution of marks. The distribution of the marks is 
shown in Fig. 3. The scale is marked on the base line and 
the number of dots above any point indicates the number 
of teachers who gave the indicated "grade." Thus the 
"grade" of 75 was given by thirteen teachers, the "grade" 
of 76 by three teachers, and so on. Of the 116 marks, two 
were above 90, while one was below 30. Twenty were 80 
or above, while twenty other marks were below 60. Forty- 
seven teachers assigned a mark passing or above, while 
sixty-nine teachers thought the paper not worthy of a 
passing mark. 

1 Starch and Elliott, "Reliability of Grading High-School Work in 
English"; in School Review, vol. 20, pp. 442-57; "Reliability of Grading 
Work in Mathematics"; in School Review, vol. 21, pp. 254-59; "Reliability 
or Grading Work in History"; in School Review, vol. 21, pp. 676-81. 



INACCURACY OF SCHOOL MARKS 9 

Not only were similar results obtained by Starch and El- 
liott in English and in history, but other investigators l 
have verified them many times. In the face of such facts 
only one conclusion is possible; namely, that under ordinary 
conditions the marks assigned to examination papers by 
teachers are very unreliable. Such marks can represent only 
very crude and very inaccurate measures of the abilities of 
pupils. It is not too much to say that the mark which a 



• ■ • • • • 

• •••• •••• 

• ••• .*••••• . • . • • • • • • » 



28 53 55 60 65 70 75 80 85 90 

Fig. 3. Distribution op Marks assigned to one Geometry Paper by 
116 Teachers. 

Passing grade 75. Range 28 to 92. Marks assigned by schools whose passing grade was 70 
were weighted by 3 points. Median 70. Probable 7.5. 



pupil receives on an examination paper depends upon the 
teacher who "grades" the paper, as well as upon what the 
pupil places upon the paper. 

It has also been shown that the same teacher is not con- 
sistent in his own marking. If a set of papers are marked a 
second time, the two sets of marks will vary widely. 2 

Summary. We have now presented an illustration of each 
of three types of evidence that teachers' marks, both final 
"grades" and examination "grades," are inaccurate. In 
each case the illustration is typical of a number of similar 
ones which might be mentioned. We have, therefore, a 

1 See Kelly, F. J., Teachers* Marks, p. 51, and following, for accounts of 
other investigations. 

2 See Starch, Daniel, Educational Measurements, p. 9. 



10 MEASURING THE RESULTS OF TEACHING 

large amount of evidence that teachers* marks are not ac- 
curate. We shall next consider two causes for the errors in 
marking examination papers. 

Conditions which contribute to the inaccuracy in marking 
examination papers. (1) Error due to unequal value of ques- 
tions. A critical study of examinations and of the manner 
of giving them reveals certain conditions which contribute 
to the inaccuracy in teachers' marks. In the first place, the 
questions are generally considered equal in value, but if we 
judge the value of questions on the basis of their difficulty 
as shown by the responses of the pupils, it is seldom that 
the same credit should be given for answering correctly two 
different questions. As evidence of this consider the follow- 
ing questions taken from an examination in United States 
history. 1 The number following the question is the per cent 
of pupils who answered the question correctly. 

To what religious body did most of the settlers of Penn- 
sylvania belong? 62 . 3 

What critical problem arose during Buchanan's adminis- 
tration? 7.0 

What is the main purpose of the Monroe Doctrine? %5.5 

These differences in the per cent of correct answers are 
merely typical of what is very likely to be the case in any 
examination prepared by the teacher. The questions will 
not be equally difficult, and it is the general practice to base 
the credit given for a correct answer upon the difficulty of 
the question : that is, less credit is given for answering cor- 
rectly an "easy" question than for a "hard" one. 

It is easy to understand how a serious element of error is 
introduced when each question is considered to have a value 
of ten points and the questions are not equal in difficulty. 

1 Buckingham, B. R., "Survey of the Gary and Prevocational Schools," 
Seventeenth Annual Report of the City Superintendent of Schools (New York 
City), 1914-15. 



INACCURACY OF SCHOOL MARKS 11 

The situation is much the same as we should have in meas- 
uring distances if yardsticks of different lengths were used, 
but were considered to be equal. Under such circumstances 
a yard would have no definite length, and to say that a cer- 
tain distance was 21.42 yards would convey no definite in- 
formation about it. For this reason the Federal Government 
has standardized all weights and measures by establishing 
definite units, and before we can obtain definite measures of 
the abilities of children, it will be necessary to devise tests 
consisting of standard units: that is, the questions or exer- 
cises composing the test must be evaluated. 

A teacher's estimate of the difficulty of questions is unre- 
liable. Can a teacher judge of the difficulty of a problem or 
even arrange a list of problems in order of difficulty? One 
investigator l studied this question by submitting the fol- 
lowing list of twenty- three problems to twenty teachers who 
were asked to estimate the per cent of pupils who would solve 
each problem correctly if given ten minutes for each. From 
this information it was possible to determine which problem 
each teacher considered easiest, which second in difficulty, 
and so on. The results of these teachers' judgments are 
given in Table I. 

1. How much change should I expect from $5, after paying for 
5 pounds of coffee at 38 cents a pound? 

2. If $1991 a day is paid to 724 men who each earn the same 
wages, how much does each man receive? 

3. A boy had 210 marbles. He lost 1/3 of them. How many 
were left? 

4. A grocer had a tank holding 44 3/16 gallons of oil. One day 
he drew out 15 3/4 gallons and the next day 9 1/8 gallons. How 
many gallons were left in the tank? 

5. There are 550 pupils on the roll. If 5/8 of them are here to- 
day, how many are absent? 

1 Comin, Robert, "Teachers' Estimates of the Ability of Pupils"; in 
School and Society, vol. 3, p. 67, January 8, 1916. 



12 MEASURING THE RESULTS OF TEACHING 

6. If 3/4 of a pound of cheese is sold for 45 cents, how much 
can be bought for $1? 

7. A storekeeper sold 12 yards of cloth, which was 4/15 of the 
whole piece. How many yards in the whole piece? 

8. A baseball team played 160 games during the season and won 
100 of them. What part of the whole number of games did the 
team win? 

9. A store takes in the following sums: $1250.50, $300, $175, 
$16.25, $120.50, $32.75, $68.50. It pays out: $600, $360, $166.67, 
$33.33, $240. How much remains after payments are made? 

10. A man bought a house for $7250. After spending $321.50 for 
repairs, he sold it for $9125. How much did he gain? 

11. A reader has 29 lines on a page and in all 10,034 lines. How 
many pages in the book? 

12. A boy lost one fourth of his kite string in a tree, one third in 
some wire, and one fifth in a hedge. What part of his string was 
left? 

13. How much will 8 3/4 dozen pencils cost at the rate of $1/4 
for half a dozen? 

14. If it takes a train three quarters of an hour to reach a certain 
station, what fraction of an hour will it take the train to go 3/5 of 
the distance? 

15. A man has a salary of $125 a month. He saves 20 per cent of 
his salary. How much will he save in a year? 

16. A workman pays $22 a month for board, which is 20 per cent 
of his wages. What are his wages? 

17. Mr. Marshall receives a salary of $2500 a year. His rent 
costs him 1 /3 of this and his other expenses are $1500. He saves 
the rest. What per cent of his salary does he save? 

18. John had $1.20 Monday. He earned 30 cents each day on 
Tuesday, Wednesday, Thursday, and Friday. Saturday morning 
he spent one third of what he had earned in the four days. Satur- 
day afternoon his father gave John half as much as John then had. 
How much did his father give John? 

19. A boy had $3. He paid it all for four articles, which we will 
call A, B, C, and D. B cost as much as D. A cost as much as B, 
C, and D together. The boy sold A and B for 1 1 /2 times what he 
paid for them. He sold C and D f or 1 1 /4 times what he paid for 
them. How much did he get for the four articles? 

20. A party of children went from a school to a woods to gather 
nuts. The number found was but 205, so they bought 1955 nuts 



INACCURACY OF SCHOOL MARKS 



13 



more from a farmer. The nuts were shared equally by the chil- 
dren and each received 45. How many children were there in the 
party? 

21. One summer a farmer hired 43 boys to work in an apple 
orchard. There were 35 trees loaded with fruit and in 57 minutes 
each boy had picked 49 apples. If in the beginning the total num- 
ber of apples on the trees was 19,677, how many were there still 
to be picked? 

22. A girl found that by careful counting there were 87 letters 
more on a page of her history than oa a page of her reader. She 
read 31 pages in each book in the first 29 days of school. How 
many more letters each day did she read in one book than in the 
other? 

23. The children of a school made small boxes to be filled with 
candy and given as presents at a school party. Six hundred boxes 
were needed. In 4 days grades 3 to 7 made 20, 25, 83, 150, and 
150 boxes. The eight grade agreed to make the rest. How many 
did the eighth grade make? 

Table I. Showing the Rank of Problems by Teachers' 
Judgments 



Bank 


Problems 


1 

4 
5 

2 

2 
2 
1 
2 
2 


2 

2 

'4 
3 
4 
3 
2 
1 

i 


3 

12 
4 

'i 

l 
l 
l 


4 

*2 

i 
l 

3 
2 

3 
2 

1 
1 
1 

'i 

i 


5 

6 

1 

3 
1 

2 
3 
1 

1 
1 


6 

i 

"i 

3 
1 
4 
4 
1 
1 
3 

i 


7 

*2 

2 

"i 

'i 

l 

o 
3 
3 
2 

1 
1 

i 


s 
i 

3 
2 

'4 

2 
1 
1 
1 
2 

2 

"\ 


9 

2 

1 
2 
1 
2 
3 
2 
2 
1 

"i 
l 
l 

i 


10 

'i 

l 

'4 

3 
2 

1 

'2 

'4 

1 

'i 


11 

'4 

2 
4 
2 
3 

1 

1 

'i 

1 


12 

'i 

i 

1 

'5 
2 
3 

i 
3 

3 


13 

i 

1 
2 
1 
4 
2 
3 

'3 

'2 

i 


14 

'2 
1 

i 
1 
2 
5 

2 
1 
1 

'2 
2 


15 

i 

'i 

3 
3 
2 
3 
2 
1 
1 

1 


16 

'2 

3 

'i 

3 

1 
2 
2 
1 
1 
1 
1 
1 
1 


17 

i 

'i 

'i 
1 
1 
3 
1 
3 

'4 
2 
2 


is 

"i 

i 

2 

'3 
2 
3 
3 
5 


19 

'i 
i 

13 


20 

i 
2 

i 

'3 
2 
1 

"<6 
1 
1 

i 


21 

i 
3 
3 

6 
6 
1 


22 

1 

5 
5 
4 
3 
1 


23 


1 
2 
3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

. 18 

19 

20 

21 

22 

23 


1 

'i 

•2 

i 

'i 
1 

1 
1 
1 

'2 

4 
3 

i 



14 MEASURING THE RESULTS OF TEACHING 

Table H. Problems ranked according to Real Difficulty 
and Teachers' Estimates 



. hf 


Bank 


Average rani. 


OOlCT/h 


(real difficulty) 


teachers' estim 


1 


3 


2 


2 


6 


4 


3 


10 


1 


4 


18 


9 


5 


2 


6 


6 


20 


18 


7 


5 


11 


8 


4 


5 


9 


11 


7 


10 


9 


8 


11 


1 


3 


12 


16.5 


13 


13 


19 


14 


14 


15 


17 


15 


8 


12 


16 


13 


10 


17 


14 


19 


18 


22 


20 


19 


23 


23 


20 


12 


15.5 


21 


16.5 


22 


22 


21 


21 


23 


7 


15.5 



Table I shows that four teachers judged Problem 1 to be 
the easiest, five judged it to be second in difficulty, two 
judged it to be third in difficulty and so on. The remarkable 
thing about this table is the lack of agreement in the judg- 
ments of the teachers. The problems are not unusual. The 
list or a portion would make a typical examination. It 
should be clear that if a teacher giving such a list attempts 
to assign values to the several questions, the values thus 
assigned are likely to be inaccurate. It is doubtful, except in 
extreme cases such as Problem 19, whether the values will 
be more accurate than if the questions are considered to be 
equal in value. 

The problems were given to the pupils in the fifth, sixth, 
seventh, and eighth grades in one school. The total number 



INACCURACY OF SCHOOL MARKS 15 

of pupils was about 1500. By doing this it was possible to 
determine what problem actually was easiest, and the order 
of difficulty for the entire list. The average rank of each 
problem as determined by the pupils' scores, and the rank 
as determined by the average of teachers' opinions, are given 
in Table II. This table presents some interesting facts. 
Twelve of the twenty teachers agreed that Problem 3 was 
easiest and no one ranked it above seventh in difficulty. Its 
real rank was found to be tenth. Similar discrepancies can be 
pointed out for other problems, although in the case of certain 
problems the average of the teachers' estimates approximates 
the real rank. Thus even the average judgment of twenty 
teachers on the relative difficulty of problems is not reliable 
and the judgment of a single teacher is much less reliable. 
(#) Rate of doing work neglected. In the second place, it is 
customary in giving an examination to allow sufficient time 
for all pupils to answer all of the questions, or if this is not 
done, the papers are graded on the basis of what each pupil 
has done. This manner of giving an examination fails to 
take into account the rate at which a pupil is able to answer 
the questions. Only the quality of the answers is considered, 
and the pupil who answers the questions with difficulty, and 
who barely finishes in the time allowed, receives exactly the 
same "grade" as the more capable pupil who is able to 
answer the questions easily and who finishes in one half or 
one third of the time, providing the two sets of answers are 
equivalent. It is clear that when this is done, the "grade" 
or mark which the pupil receives is not a true measure of his 
ability, because the rate at which he is able to do work is 
a "dimension" of his ability as well as the quality of what 
he does. In certain cases the rate may be a relatively un- 
important dimension. Neglecting it in measuring the ability 
of a pupil is much like neglecting the width in measuring a 
rectangle to determine its area. 



16 MEASURING THE RESULTS OF TEACHING 

Some may insist that it is unfair to the slow-working pupil 
not to allow sufficient time for him to answer all of the ques- 
tions. However this may be, it certainly is unjust to the 
more capable pupil to deprive him of the opportunity to 
demonstrate what he is able to do. This is exactly the case 
when the work asked of him is sufficient to keep him em- 
ployed only a half or a third of the period allowed for the 
examination. This practice of ignoring the rate of working 
probably tends to cause desultory and careless school work. 

Investigation has shown that rapid work and a high de- 
gree of quality or accuracy are not incompatible in arith- 
metic. The same statement can be made with reference to 
reading. Investigation has indicated that a considerable per 
cent of pupils can be made more accurate in arithmetic by 
forcing them to work more rapidly. It has also been shown 
that about three pupils out of four make progress in rate of 
work and accuracy at the same time. In view of these facts, 
it appears that good instruction requires that the teacher 
give attention to the rate of doing work as well as to the qual- 
ity of the work done. The rate at which a pupil is able to do 
work of a given quality is as much a factor of his ability as 
is the quality of the work which he does. 

The rate at which a pupil works can be measured very 
easily. It is simply necessary to secure a record of the time 
which he spends in answering the set of questions. When an 
examination is given to a group, it is rather inconvenient 
to secure a record of the time which each pupil spends upon 
the examination. However, one can secure just as true a 
record of the rate at which each pupil works by making the 
examination long enough so that no pupil finishes in the 
time allowed. For each pupil the number of minutes, di- 
vided by the number of units of work which he did, will give 
his rate of working per unit. 

Summary. In the preceding pages we have shown, first, 



INACCURACY OF SCHOOL MARKS 17 

that questions differ in difficulty and that teachers cannot 
judge their relative difficulty with reliability; and, second, 
that the rate of doing work, which is in many cases an im- 
portant "dimension" of ability, is commonly neglected in 
giving examinations. The first of these conditions con- 
tributes to the inaccuracy of marking examination papers. 
The second means that the examination paper frequently is 
not a true record of the pupil's ability. This happens when 
the pupil finishes before the end of the period allowed. There 
are two other points which should be mentioned in this con- 
nection. Marks placed upon examination papers do not 
have a definite meaning because a wide range of topics is 
included within a single examination and because no reli- 
able standards exist. 

Wide range of topics included within an examination 
makes the "grade" have an indefinite meaning. Examina- 
tions are usually made up of questions from a number of 
different fields within a subject. Take, for example, the 
following examination in arithmetic which was given to a 
sixth-grade class: 

1. Write in Roman system: 49, 79, 94, 96, 146. 

2. If 11 A. of land are worth $1485, what is one acre worth? 

3. If a desk is 4 2/3 ft. long and 3 5/12 ft. wide, what is the 
perimeter? 

4. How much must you add to 26 7/8 in. to make a yard? 

5. A man has to travel 117 mi. After going 5/9 of the distance, 
how many miles has he still to travel? 

6. The perimeter of a square is 851 in. What is the length of 
one side? 

7. Of 152 chickens a hawk captured 12 1/2%. How many were 
captured? How many were left? 

8. A man saves $675.20 a yr., which is 32% of his income. How 
much is his income? 

9. At $1.38 a yd., what will 37 yds. of carpet cost? 

10. At $65.50 an acre, what must a man pay for 25.4 acres of 
land? 



18 MEASURING THE RESULTS OF TEACHING 

Question 1 calls for a knowledge of Roman numerals; 
Question 2 asks the pupil to find the cost of a unit when the 
cost of the whole is given; Questions 3, 4, and 6 deal with 
mensuration; Question 5 calls for the finding of a fractional 
part of the whole; Questions 7 and 8 are problems in buying. 
Thus we find six different topics included within an exam- 
ination of ten questions. 

Suppose a pupil receives a "grade" of 80 on this exami- 
nation. Even if 80 is an accurate measure of what the 
pupil is able to do on this examination, it cannot have a 
definite meaning. It does not tell us whether the pupil 
lacks ability in the field of Roman numerals, or in the field 
of percentage, or in some other of the fields included in 
this examination. In order that the total score made on 
an examination may be a definite measure of a pupil's 
ability, the questions which compose it must be drawn from 
a single field, or at most from a small group of closely related 
fields. If this is not done, the scores for each question must 
be kept separate in order to have a definite meaning. 

The situation is much the same as if the length, width, 
height, seating capacity, number of windows, and the num- 
ber of doors of a room were added together to form a measure 
of the room. If we assume that each of these characteristics 
of the room was measured with a high degree of accuracy, 
the total of the numbers expressing the measures gives us 
only very general information about the room. If the total 
is large, we know that the room is probably large; if the total 
is small, we know that it is small. But under no circum- 
stances can we be certain that the room has any windows 
or doors, that it contains any seats, or that its dimensions 
are well proportioned. In order that we may have definite 
information about the room, it is necessary that the meas- 
ures of the several characteristics be kept separate. 

No standards for interpreting measures. The fact that 



INACCURACY OF SCHOOL MARKS 19 

a seventh-grade pupil solves correctly eight problems out 
of seventeen or spells correctly twenty-one words out of 
twenty-five has a meaning only by comparison with the 
standard for these examinations. By standard we mean 
the number of problems which a pupil of a given grade, in 
this case the seventh, should do correctly when given this 
examination. If the standard is twelve problems, this pupil 
is below seventh-grade standard in ability and has not done 
satisfactory work. On the other hand, if the standard is six 
problems, this pupil is above standard and possesses superior 
ability. Without a standard a teacher cannot know what a 
measure means. 

The above statement may not appear to be true at first 
thought. Standards have not been determined for the exam- 
inations which a teacher gives, but he "guesses" what the 
standard should be when the questions are made out and 
the examination is judged by the teacher to be "fair" for 
the pupils of that grade or one "they should be able to 
pass." We have just seen how unreliable teachers' judgments 
are with reference to the difficulty of problems in arithme- 
tic. Their "guesses" with reference to standards appear to 
possess about the same degree of reliability. 

Accurate measurements of the abilities of pupils may be 
made by using standardized tests. The preceding pages 
were written to make clear that our present measurements 
of the abilities of pupils were inaccurate and hence unsat- 
isfactory. Since the measurement of results is very neces- 
sary to both the teacher and the supervisor, there is a need 
for instruments with which accurate measurements can be 
made. Standardized tests are such instruments and in the 
following chapters certain ones will be described and direc- 
tions given for their most effective use by the teacher. 

Standardized tests have been scientifically devised. The 
questions or exercises which make up the tests have been 



20 MEASURING THE RESULTS OF TEACHING 

carefully selected and evaluated. Directions have been 
provided so that different teachers will assign the same mark 
to the same paper. The rate of work is measured where it is 
an important "dimension" and the tests have been stand- 
ardized. Generally a standardized test is limited to a single 
topic or to a small group of topics so that a pupil's score has 
a definite meaning. These features eliminate the defects in 
ordinary examinations which have been discussed in this 
chapter and hence constitute reasons for the use of stand- 
ardized tests. 

Other advantages in using standardized tests. Standard- 
ized tests are helpful in another way to the teacher, partic- 
ularly the rural teacher who must work isolated for the most 
part from other teachers. The standards of such tests are 
definite objective aims stated in a way that both teacher 
and pupil can understand. The value of a definite standard 
can hardly be overestimated. As we shall show later it fur- 
nishes a strong motive. It also guides one's efforts. It makes 
possible economy of time by limiting training. The use of 
standardized tests directs attention to the results which are 
to be attained. Too often attention has been focused upon 
the method being used rather than upon the results. A third 
advantage is due to the fact that the patrons of the school 
are interested in definite statements of results, particularly 
when those results can be compared with recognized stand- 
ards. Many objections to a teacher or a school have been 
answered by the accurate measurement of results. The 
writer has heard one superintendent state that standardized 
tests would be worth using if they did nothing more than 
stop the mouths of those who are accustomed to complain 
about what the public school is doing. 



INACCURACY OF SCHOOL MARKS 21 

QUESTIONS AND TOPICS FOR STUDY 

1. What evidence do we have for showing that "final grades" are inac- 
curate measures of the abilities of pupils? 

2. How do we know that the marking of examination papers is in- 
accurate? 

3. What factors contribute to this inaccuracy? Can you think of any 
not mentioned in this chapter? 

4. Have you ever felt that examination marks were inaccurate? Why? 

5. Ask several teachers to " grade" the same set of papers and compare 
the "grades" given to each paper? 

6. What is meant by saying that a "grade" has an indefinite meaning? 

7. What is a standard? Why are standards needed? 

8. What are the advantages of using standardized tests? 

9. The unreliability of individual judgment may be shown by having a 
group of persons guess the length of a stick when it is held as much 
as ten feet away from them. 

10. What is meant by saying that the rate of doing work is a "dimen- 
sion" of a pupil's ability? Why is it important to measure it? 



CHAPTER n 

THE MEASUREMENT OF ABILITY IN READING « 

There are two types of reading, silent reading and oral 
reading. In reading silently one is concerned primarily 
with understanding the printed page. In oral reading the 
point of emphasis is the communication of the meaning by 
means of oral expression. Both kinds of reading are taught 
in the school, and the first step in the measurement of ability 
in reading is to recognize the existence of the two types of 
reading ability. We shall consider their measurement in 
two separate sections. 

I. Silent Reading 
1. Monroe 9 s Standardized Silent Reading Tests 

Ability to read silently is measured by having the pupil 
read a selection and then give evidence of the degree of his 
understanding or comprehension of the material read. One 
method of securing this evidence is to require the pupil to 
answer one or more questions based upon what he has read. 
This plan may be illustrated by the following paragraph 
and question. Answering the question requires that the 
pupil comprehend the principal idea of the exercise. 

Not far from Greensburg is a little valley, among the high hills. 
A small brook glides through it, with just murmur enough to lull 
one to repose; and the occasional whistle of a quail, or tapping of 
a woodpecker, is almost the only sound that ever breaks in upon 
the uniform tranquillity. 

1 The reader should have a copy of each of the standardized tests de- 
scribed in this and the following chapters. In several instances it will 
be almost impossible to understand the discussion without a copy of the 
test at hand. See the Appendix for directions for securing a sample package 
and for purchasing any of these tests for class use. 



MEASUREMENT OF ABILITY IN READING 23 

What kind of a picture do you get from reading the above 
paragraph? 

disorder activity noise calmness confusion 

This exercise is expressed in such a way that the pupil will 
have no difficulty in expressing his answer if he knows what 
it is, and also his answer will be either right or wrong. There 
can be no difference of opinion in marking the exercise. 
A series of tests, known as Monroe's Standardized Silent 
Reading Tests, consists of a number of such exercises. The 
exercises were taken from school readers and other books 
that children read which insures that they present typical 
reading situations. The amount of credit to be given a pupil 
for doing each exercise correctly has been scientifically de- 
termined and is called the comprehension value. The sum of 
the comprehension values of the exercises done correctly in 
five minutes makes the pupil's comprehension score. This 
score is the measure of his ability to comprehend or under- 
stand the exercises of the test. 

The pupil's rate of reading is important as well as the de- 
gree of his understanding. For this reason each exercise has 
a rate value, and a pupil's rate score is the sum of the rate 
values of the exercises which he tries in five minutes regard- 
less of whether he does them correctly or not. This value 
has been so chosen that it represents the number of words 
which the pupil reads per minute. A pupil's rate score is the 
measure of his rate of reading. 

Test I of the series is for Grades III, IV, and V, Test II 
for Grades VI, VII, and VIII, and Test III for Grades IX 
to XII. There are three forms of Tests I and II which are 
equivalent in difficulty, so that when it is desired to measure 
the ability of the pupils a second or third time it is not 
necessary to use the same exercises. A few exercises of 
Test II are reproduced to illustrate more fully this type 
of silent reading test. 



24 MEASURING THE RESULTS OF TEACHING 



Rate 

Value 
7 



Rate 

Value 

8 



Rate 

Value 

ii 



Rate 

Value 
17 



NO. 2 

At evening when I go to bed 
I see the stars shine overhead; 
They are the little daisies white 
That dot the meadow of the night. 

What are the little white daisies of the night? 



No. 4 

They rested and talked. Their talk was all 
about their flocks, a dull theme to the world, 
yet a theme which was all the world to them. 

What do you suppose was the occupation of 
these men? 

carpenter doctor merchant 

shepherd blacksmith 



No. 7 

He was a wicked ruler who, with his still 
more wicked sons, oppressed and wronged the 
people in many ways. 

If the people would be sorry when the ruler 
and his sons died, draw a line under the word 
ruler; if they would be glad, cross out the word 
ruler. 

ruler 



No. io 

It was cold, bleak, biting weather; foggy 
withal; and he could hear the people in the 
court outside go wheezing up and down, beat- 
ing their hands upon their breasts and stamp- 
ing their feet upon the pavement-stones to 
warm them. 

The author has attempted to give you a 
picture in this paragraph. After reading the 
paragraph, if you think it is a picture of com- 
fort and pleasantness, draw a line under the 
word hear; if of cheerlessness and dreariness, 
draw a line under bleak. 

hear wind bleak cold 



MEASUREMENT OF ABILITY IN READING 25 

Directions for using the tests. Detailed directions for 
giving these tests are printed on the first page of the test 
paper and hence it is not necessary to reproduce them here. 
However, there are four general rules which should be fol- 
lowed in the giving of all standardized tests: (1) Follow the 
printed directions carefully. Do no more or no less than the 
directions specify. Do not try to improve upon the direc- 
tions. Comparisons of the scores of your pupils with the 
scores of other classes and with the standard scores will not 
be valid if the printed directions are not followed, because 
these scores were obtained according to these conditions. 
(2) Be careful to allow exactly the number of minutes speci- 
fied — five minutes. Use a watch with a second-hand or a 
stop-watch if one is available. (3) The examiner should ex- 
ercise care not to excite or frighten the pupils by his manner 
of giving the tests. He should not be in a hurry. He should 
not be cross. He should remember that reliable measure- 
ments of the abilities of the pupils will not be obtained unless 
the pupils work naturally. (4) Study the directions for the 
tests until you are familiar with them. It is wise to go 
through the directions at least once imagining that you have 
the class before you. Your failure to be familiar with the 
directions may affect the scores of your pupils. 

Giving the tests in rural schools. These silent reading 
tests may be given to a group of pupils belonging to several 
different grades as easily as to a group belonging to a single 
grade. It is only necessary to see that each pupil is pro- 
vided with the test which is designed for his grade. The 
time allowance is the same for all grades. In a rural school 
it will be most convenient to test all of the pupils above the 
second grade at one time. In recording the scores it will, of 
course, be necessary to record the scores for the different 
grades separately. 

When the tests should be given. These silent reading 



26 MEASURING THE RESULTS OF TEACHING 

tests are not teaching devices. They are instruments for 
measuring the ability of pupils to read silently. They should 
be given at the beginning of the school year so that the 
teacher may know his pupils better. If they are not used at 
the beginning of the year, they may be given at any time, 
preferably as early as convenient. The tests should be re- 
peated at the end of the year so that the teacher may know 
how much his pupils have increased their ability to read 
silently. When the tests are given a second time a different 
form should be used. If it is desired, the tests may be given 
a third time at the middle of the year, but they should not 
be given more than three times a year. 

Scoring the test papers. The correct answer for each ex- 
ercise is given on the back of the class record sheet which is 
always furnished with the tests. It is most satisfactory for 
the teacher to mark the papers, but if the teacher feels that 
he cannot take the time for it he may read the answers 
and have the pupils mark their own papers, or better, have 
them exchange papers. In any case the teacher should ex- 
amine enough of the papers to make certain that they have 
been marked correctly. The question has been asked, 
"Should the pupils be required to give their answers in the 
form of complete sentences ?" This is not required. The 
author does not believe that it is wise to insist upon this 
form. 

Good arrangement of scores. The significance of a group 
of facts, such as the scores made by a class upon a test, may 
be made more evident by certain methods of arranging 
them. Take, for example, the comprehension scores which 
were made by a sixth-grade class of thirty-five pupils when 
given a certain silent reading test. When these scores are 
presented in the manner of Table III, the array tends to 
confuse. One must scan the entire array to learn that the 
lowest score is 4.2, or that the highest score is 30.1. One 



MEASUREMENT OF ABILITY EST READING 27 

cannot easily learn that pupil BB, who made a score of 14.9, 
stands eighth from the poorest in the group. If now the 
scores are simply rearranged in order of magnitude, as shown 
in Table IV, their significance is much more easily grasped. 

Table HE. Showing a Poor Arrangement of Scores 



Pupil 


Score 


Pupil 


Score 


Pupil 


Score 


A 


27.3 


M 


10.0 


Y 


16.0 


B 


19.2 


N 


16.3 


Z 


19.1 


C 


26.2 





21.1 


AA 


15.4 


D 


22.5 


P 


25.6 


BB 


14.9 


E 


15.4 


Q 


21.1 


CC 


16.4 


F 


18.3 


R 


15.9 


DD 


14.1 


G 


28.4 


S 


16.1 


EE 


4.2 


H 


17.4 


T 


5.9 


FF 


20.0 


I 


25.1 


u 


30.1 


GG 


24.1 


J 


15.7 


V 


22.3 


HH 


26.3 


K 


11.8 


w 


13.1 


II 


25.8 


L 


21.6 


X 


12.8 







Table IV. Showing the Same Scores rearranged in a 
Better Order 



Pupil 


Score 


Pupil 


Score 


Pupil 


Score 


EE 


4.2 


Y 


16.0 


V 


22.3 


T 


5.9 


S 


16.1 


D 


22.5 


M 


10.0 


N 


16.3 


GG 


24.1 


K 


11.8 


CC 


16.4 


I 


25.1 


X 


12.8 


H 


17.4 


P 


25.6 


w 


13.1 


F 


18.3 


11 


25.8 


DD 


14.1 


Z 


19.1 


C 


26.2 


BB 


14.9 


B 


19.2 


HH 


26.3 


AA 


15.4 


FF 


20.0 


A 


27.3 


E 


15.4 


O 


21.1 


G 


28.4 


J 


15.7 


Q 


21.1 


U 


30.1 


R 


15.9 


L 


21.6 







Recording the scores. For securing a good arrangement of 
the scores obtained by using Monroe's Standardized Silent 
Reading Tests the class record sheet shown on page 28 is 
used. It will be noted that the scores are arranged in order 
of magnitude by groups. This kind of an arrangement of 
scores is called a distribution. For comprehension, all of 
the seores from 3.0 to 3.9 are grouped together. The dif- 



28 MEASURING THE RESULTS OF TEACHING 



Kate Score 


Comprehension Score 


Interval 


Number 

of 

Pupils 


Interval 


Number 

of 
Pupils 


Above 160 
141 to 150 




80 & above 
70 to 79.9 
60 to 69.9 
50 to 59.9 
45 to 49.9 
40 to 44.9 
35 to 39.9 
30 to 34.9 
27 to 29.9 
24 to 26.9 
21 to 23.9 
18 to 20.9 
15 to 17.9 
13 to 14.9 
11 to 12.9 
9 to 10.9 
7 to 8.9 
5 to 6.9 
4 to 4.9 
3 to 3.9 
2 to 2.9 
1 to 1.9 
to .9 








151 to 160 
131 to 140 
121 to 130 
116 to 120 
111 to 115 
106 to 110 
101 to 105 
96 to 100 
91 to 95 
86 to 90 
81 to 85 
76 to 80 
71 to 75 
66 to 70 
61 to 65 
56 to 60 
51 to 55 
46 to 50 
41 to 45 
36 to 40 
31 to 35 
26 to 30 
21 to 25 
16 to 20 
Below 15 








































































































Total 




Total 




Median 




Median 





Fig. 4. Showing Form used in recording 
the Scores obtained by using Monroe's 
Standardized Silent Reading Tests. 



ference between 3.0 
and 3 .9 (more exact- 
ly 3.9999-) or 1, 
is called the width 
of the interval. On 
this record sheet all 
of the intervals do 
not have the same 
width. For exam- 
ple, the interval 
from 24.0 to 26.9 
has a width of 3. 
Detailed directions 
for recording the 
scores are printed 
on the class record 
sheet and need not 
be repeated here. 

The central tend- 
ency of a distribu- 
tion. Ordinarily the 
scores of a class will 
be distributed over 
several intervals of 
the class record 
sheet. If one wishes 
to compare the 
standing of the class 
as a whole with the 
standard, it is ne- 
cessary to obtain a 
central tendency of 
the distribution. The 
central tendency 



MEASUREMENT OF ABILITY IN READING 29 

which is best known by teachers is the average, but if 
one or two pupils make very low scores they will bring the 
average down. For this reason the median is used in- 
stead of the average. The median is the value of the middle 
score of the distribution. The median score for comprehen- 
sion is found by arranging the test papers according to the 
size of the comprehension scores. When the test papers are 
arranged in order, the score on the middle paper is the me- 
dian score. For example, if there are thirty-five papers in 
the pile, the score on the eighteenth paper is the median 
score. If there are thirty-six papers, the median score is 
halfway between the score on the eighteenth paper and the 
score on the nineteenth paper. The median score for rate is 
found the same way. The median scores are called the class 
scores. 

Summary. We have described Monroe's Standardized 
Silent Reading Tests, the directions for giving them, for re- 
cording the scores and for finding the class scores. In the 
next chapter we shall take up the meaning or interpretation 
of the scores and what a teacher should do to correct the 
conditions which the tests reveal. 

2. Courtis's Silent Reading Test No. 2 

Description of the test. This test, which is to be used in 
Grades 2 to 6 inclusive, is designed to measure "the ability 
to read silently and understand a simple story and simple 
questions about the story." It consists of a connected story 
of the kind that children enjoy reading. The first two para- 
graphs of Part I of the test are reproduced on page 30 to 
show the type of story and its arrangement. 

The pupils are directed: "Read silently, and only as fast 
as you can get the meaning; for when you have finished you 
will be asked to answer questions about what you have read. 
You will be marked for both, how much you read and how 





V C v >> o 




T5T3 f\^ 




^ u. 7^ -M 




&> QJ V 4-a 






■H ph O'H 


e 


as warm and 

bloom, our child 

lawn. Every lil 

was invited. Be 

bby carried them 




plan 

colo 

dan 


3 

i 




Daddy 
th gay- 
's and 
supper 
Id. 


-a 




:ame, 
it wi 
game 
ious 
ry chi 


spring sun w 
had begun to 
•ty out on the 
o lived nearby 
tations and Bo 




arty c 
tied 

o be 
delic 

>r eve: 


O 




y of the p 
d Mother 
e were t 

and a 
flowers fc 

(30) 


<L> 


the 
3wers 
ay-pai 
irl wh 
e invi 




a a H ^**-« 


4J 

3 


• 


the d 

ole ai 

The 

gras 

fullo 


O) 


c^S ^52 


c Q- . ^ -M 

r* • en ^ (u 




Whe 
spring 
had a 
boy or 
wrote 


o 

J3 


Whe 
May 

ibbon 

n th 

bask< 




-M 


cj pw O c3 




IQ CO *H O CI 

r* <M CO CO 




s s § a s 



MEASUREMENT OF ABILITY IN READING 31 

well you understand it, but it is better to get the meaning 
of the story than to read too fast." 

The pupil reads silently for three minutes, but at the end 
of each half -minute a signal is given, and he is to mark the 
last word he has just read and to keep on reading. At the end 
of three minutes the pupil turns to Part II. This consists of 
the same story with questions based upon it. The first two 
paragraphs and the questions upon them are reproduced. 

When the spring sun was warm and the spring flowers had begun 
to bloom, our children had a May-party out on the lawn. Every 
little boy or girl who lived nearby was invited. Betty wrote the 
invitations and Bobby carried them to the children. 

A. Did the children have a May-party? 

B. Was it Bobby who wrote the invitations? 

C. Was the party held in the house? 

D. Were only girls invited to the party? 

E. Had the spring flowers begun to bloom? 

When the day of the party came, Daddy planted a May-pole 
and Mother tied it with gay-colored ribbons. There were to be 
games and dances on the grass and a delicious supper, with a 
basket full of flowers for every child. 

1. Were the children to have anything to eat? 

2. Were they going to play on the grass? 

3. Were they going into the house to dance? 

4. Were the baskets to be full of flowers? 

5. Was it Daddy who tied the ribbons to the pole? 

The measures of the pupil's ability to read silently and 
answer questions. The pupils are given five minutes to an- 
swer as many of the questions as they can. The measure of 
their understanding of the story is expressed in terms of the 
number of questions answered and the index of comprehen- 
sion. This index is found as follows: "Subtract the wrong 
answers from the right answers. (If there are more wrong 
than right, find the difference and give it a negative sign.) 
Divide the difference by the number of right answers, 



32 MEASURING THE RESULTS OF TEACHING 

carrying the result to three places and keeping two." This 
calculation is made from a table so that the labor involved is 
reduced to a minimum. 

In addition to these two scores, the number of words read 
per minute is obtained from the first part of the test. This 
is a measure of the pupil's rate of reading. 

Directions for using Courtis's Silent Reading Test No. 2. 
Detailed directions for giving the test have been prepared 
by the author of the test. These do not need to be repeated 
here, but the general directions mentioned on page 25 apply 
to these tests as well. Courtis says: 

The instructions given in this folder must be followed exactly 
if the results secured are to be compared with results from the 
same tests in other schools. The examiner needs to prepare him- 
self for his work by careful study and practice. 

The important conditions to be controlled are timing, instruc- 
tions, and manner. Keep exact times. Say no more to the children 
about the tests than is provided for in the instructions below. 
Give the instructions energetically, but easily and pleasantly. Do 
not hurry, do not get excited, do not be cross with the children. 
The children will make the best scores if they enjoy the tests and 
work naturally. 

Directions for using Courtis's Silent Reading Test No. 2 
in rural schools. Since the same test is given to all pupils in 
Grades 2 to 6, the procedure for giving the test is always the 
same and therefore it may be used as easily in rural schools 
as in graded schools. The only difference comes in recording 
the scores. Then the teacher must first be careful to have 
the test papers grouped correctly by classes or grades. 

Scoring the test papers. An answer card and detailed di- 
rections are furnished with the tests. The most accurate 
results are obtained when the test papers are scored by the 
teacher, but Courtis says: "A teacher might better give her 
time to studying the results than waste it on scoring." His 
plan is to have the scoring done by the pupils in the fifth 



MEASUREMENT OF ABILITY IN READING 33 

and sixth grades and by the seventh- and eighth-grade 
pupils in the case of pupils below the fifth grade. The scores 
of a pupil are recorded on an individual record card which is 
more convenient to handle in recording the scores of the 
class on the class record sheet. 

Recording the scores. The three scores, rate of reading 
(words per minute), number of questions, and the index of 
comprehension are recorded on the forms marked Table 1 and 
Table 3 in Fig. 5. The form of Table 1 is similar to that used 
for recording the scores of Monroe's Standardized Silent 
Reading Tests. However, it should be remembered that in 
Table 1, means to 19, 20 means 20 to 39, and so on. 
Table 3 represents a different type of form for recording 
scores. The test papers, or in this case the individual cards 
containing the record of the pupils' scores, are first sorted 
into piles according to the number of questions answered, 
putting into the first pile all the cards having a score of 
to 4 questions answered, into the second pile all those cards 
having a score of 5 to 9 questions answered, and similarly 
for the other intervals. Then each of these piles is sorted 
according to the "index of comprehension." Suppose there 
are seven cards in the pile of forty-five to forty-nine ques- 
tions answered and that these have the following "indices of 
comprehension " : - 15, 20, 47, 58, 73, 79, 80. The entries for 
these scores would be made on the "45 fine." To record the 
— 15 score, a 1 is placed in the "Less than —5" column; to 
record the 20 score a 1 is placed in the "6-39" column; to 
record the 47 and 58 scores a 2 is placed in the "40-69" 
column; and so on. 

Distributions and central tendencies. The column and 
line marked "Total" in Table 3 are filled in by finding the 
sum of the scores recorded in the respective lines or columns. 
These two sets of sums form the distributions for "number 
of questions answered" and "index of comprehension." 



34 MEASURING THE RESULTS OF TEACHING 



Table 1 



Rate of 
Heading 



Table 3 
Index of Comprehension 



se 
S.5 

£ u 
BD 


J. to 

'3- 

°sg 

■S * 3 


Over 




400 




380 




360 




340 
320 





300 




380 




360 




340 




320 
300 





280 




260 




240 
220 





200 
180 
160 
140 





120 




100 




80 
60 





40 




20 









Total 
Median 






Diagnosis 


' Guesswork 


to in pre hen si on poor : 
additional training 
needed 


Comprehen- 
sion satis- 
factory 


O L. 

e an 
S S 


"3 

o 


s 


+ 

o 


4 


CO 


t- 


CD 


OS 
f 

00 


Ml 

o 


3 


o 




70 


























65 
























6 


60 
























1 

■ 


65 
























i 


50 
























9 


45 
























"1 


40 


























35 


























30 


























25 
























i 

n 


20 


























15 


























10 
























*1 

"el 


5 
























5=3 
I'd 
H4 



























• 

1 


Total 
























s 


























_ , 



Median Number of Last Question Answered 

Median Index of Comprehension 

Fig. 5. Showing Forms used in recording the Scores obtained by 
using Courtis's Silent Reading Test No. 2. 



. 



MEASUREMENT OF ABILITY IN READING 35 



The numbers in the column headed "Number of children 
making each score'' in "Table 1" form the distribution for 
the rate of reading. The central tendency of the distribution 
which is used to describe the achievement of the class as a 
whole is the median the same as was used for Monroe's 
Standardized Silent Reading Tests. It may be found in the 
same way, although the directions given by Courtis differ 
slightly. * « 

Summary. In the preceding pages we have described 
Courtis's Silent Reading Test No. 2 and the general di- 
rections for giving it and for handling the scores. De- 
tailed directions are given in the folders, B and D, which 
should be secured when the test is purchased for classroom 
use. 

Comparison of the two silent reading tests. In comparing 
the two silent reading tests which we have just described, it 
must be remembered that they probably do not measure 
the same type of silent reading ability. We cannot, there- 
fore, compare them as we might two things of the same kind, 
as we might two makes of the same type of automobile. 
The situation is much like comparing a pleasure car with a 
truck. However, certain points may be noted. Courtis's 
test is to be used in Grades 2 to 6, while Monroe's tests are 
to be used in Grades 3 to 8. Thus a second-grade teacher 
would choose Courtis's test. Some claim that it is more sat- 
isfactory for the third and fourth grades, but that Monroe's 
test should be used beginning with the sixth grade. Of the 
two tests, Monroe's takes less time and is simpler to under- 
stand and use. For the teacher who is inexperienced in the 
use of standardized tests this is an important consideration. 
However, it is frequently profitable to give both tests. One 
will supplement the other. 



36 MEASURING THE RESULTS OF TEACHING 

3. Thorndike's Visual Vocabulary Scale 

Need for a vocabulary test. When a pupil makes a silent 
reading score which is below standard, it may be due to any- 
one of several causes or to a combination of causes. One 
important cause and one which frequently occurs is the 
pupil's failure to comprehend the meaning of the words. 
Understanding the meaning of a paragraph requires the 
ability to comprehend the meaning of the individual words. 
Hence a vocabulary test furnishes a means for obtaining 
information which may reveal the cause of the pupil's low 
score in silent reading. 

Description of the test. This test can be most satisfac- 
torily described by reproducing a portion of it. Each pupil 
is given a test paper on which are printed the following 
directions and lists of words. 

Thorndike Reading Scale B. Word Knowledge or Visual 
Vocabulary — Series X 

Write the letter W under every word that means something about 

war or fighting. 
Write the letter B under every word that means something about 

business or money. 
Write the letters CHU under every word that means something 

about church or religion. 
Write the letter R under every word like father or wife that means 

something about relatives or the family. 
Write the letters COL under every word that means a color. 
Write the letter T under every word like now or then that means 

something to do with time. 
Write the letter D under every word like here or north that means 

something about distance or direction or location. 
Write the letter N under every word like ten or much that means 

something about number or quantity. 

4.0 camp, flag, west, mother, two, general, green 
troops, south, fort 



MEASUREMENT OF ABILITY IN READING 37 

4.5 gray, cousin, pink, uncle, yellow, hour, pay, 
aunt, early, commander 

5.0 marriage, defeat, many, afternoon, guard, buy, 
captive, military, relation, late 

6.0 hymn, defend, across, merchant, noon, forty, 
conquer, dagger, profit, Tuesday 

There are eight other lists which gradually increase in 
difficulty. The scale values of the several lines printed in the 
left margin were determined by having several thousand 
children undertake to indicate the meaning of each word. 
The greater the per cent of children who could not indicate 
correctly the meaning of the word, the higher the value at- 
tached to the word. The pupil's score is the value of the 
most difficult list in which he marks correctly eight out of 
the ten words. Likewise the class score is the value of the 
list for which the class averages 80 per cent (8 out of 10) of 
correct meanings. 

Giving the test. Detailed directions for giving this test are 
printed on the cover of the test. 1 It is, therefore, necessary 
only to remind the reader that the general directions on 
pages 25 and 32, with reference to following directions and 
the manner of presenting the tests to the pupils, apply. 

Recording the scores. The class record sheet devised by 
Thorndike called for a detailed record for each pupil. This 
was cumbersome to use and required more labor than ap- 

1 This is not true of the form of the test which is secured from the 
Bureau of Publications of Teachers College, but is true of the form dis- 
tributed by the Bureau of Educational Measurements and Standards, 
Emporia, Kansas. . 



38 MEASURING THE RESULTS OF TEACHING 

peared to be justified for obtaining the class score. A simpler 
class record sheet has been designed by the writer. This is 
reproduced in Fig. 6. Directions for recording the scores on 



Line value 


Number of words wrongly marked or 
omitted 


Total 


Per cent 


4.0 








4.5 








5.0 








6.0 








6.5 








7.0 
7.5 
8.0 




















8.5 








9.0 








9.5 








10.0 

















Class Score. 



Fiq. 6. Record Sheet for recording Scores obtained by using 
Thorndike's Visual Vocabulary Scale. 



MEASUREMENT OF ABILITY IN READING 39 

this sheet and for calculating the class score are printed on 
the back of it and thus need not be reproduced here. The 
calculation of the class score may appear to be difficult to 
understand, but if the directions are studied carefully and 
followed a step at a time, one should soon learn how to do it. 

II. Oral Reading 
1, Gray's Oral Reading Test 

Description of the test. For measuring the ability of 
pupils to read orally, Gray has devised a test consisting of 
a series of paragraphs arranged in order of gradually in- 
creasing difficulty in oral reading. The test is designed to 
be used in all grades beginning with the first. The nature 
of the test can best be illustrated by reproducing a few of 
the paragraphs: 

I. A boy had a dog. 

The dog ran into the woods. 

The boy ran after the dog. 

He wanted the dog to go home. 

But the dog would not go home. 

The little boy said, "I cannot go home without my dog." 

Then the boy began to cry. 

6. It was one of those wonderful evenings such as are found only 
in this magnificent region. The sun had sunk behind the moun- 
tains, but it was still light. The pretty twilight glow embraced a 
third of the sky, and against its brilliancy stood the dull white 
masses of the mountains in evident contrast. 

II. The hypotheses concerning physical phenomena formulated 
by the early philosophers proved to be inconsistent and in general 
not universally applicable. Before relatively accurate principles 
could be established, physicists, mathematicians, and statisticians 
had to combine forces and work arduously. 

Giving the test. In giving the test the pupils are taken one 
at a time and asked to read beginning with the first para- 
graph. As the pupil reads, the teacher records on another 



40 MEASURING THE RESULTS OF TEACHING 

copy of the test, two sets of facts: the number of seconds 
the pupil takes to read each paragraph and the errors which 
are made. To obtain the number of seconds the teacher 
must have a watch with a second-hand or, better, a stop- 
watch. Six types of errors are recorded: (1) complete mis- 
pronunciation of a word so as to indicate that the pupil has 
no control over it; (2) partial mispronunciation; (3) omis- 
sions; (4) substitutions; (5) insertions; and (6) repetitions. 
The method of marking these errors on the test paper is 
illustrated in the following quotation from the class record 
sheet: 

The sun pierced into my large windows. It was the opening 
of October, and th^sky was(oya dazzling blue. I looked out of 
toy wfodow(an<i)down the street. The white houseQof the long, 
straight street were (almost painful to the eyes. The clear 
atmosphere allowed full play tQ&§ s^m^J>rightness. 

If a word is wholly mispronounced, underline it as in the case of 
"atmosphere." If a portion of a word is mispronounced, mark ap- 
propriately as indicated above: "pierced" pronounced in two syl- 
lables, sounding long a in "dazzling," omitting the 5 in "houses" 
or the al from "almost," or the r in "straight." Omitted words are 
marked as in the case of "of" and "and"; substitutions as in the 
case of "many" for "my"; insertions as in the case of "clear" 
and repetition as in the case of "to the sun's." Two or more 
words should be repeated to count as a repetition. 

To give the test satisfactorily requires practice in detect- 
ing the errors and in recording them. The teacher should 
have some one read the test, intentionally making errors, 
so that he may become skillful in giving it. 

The pupil's score. The pupil's score depends upon both 
the number of seconds he takes to read the different para- 



MEASUREMENT OF ABILITY IN READING 41 

graphs and the number of errors which he makes. For ex- 
ample, certain credit is given a second-grade child for read- 
ing paragraph 1 in forty seconds with less than five errors, 
and additional credit is given the same child for reading the 
same paragraph in thirty seconds with less than five errors, 
or in forty seconds with less than four errors. Still different 
credit is given to third-grade children for each of the above 
achievements with paragraph 1. When the combination of 
length of time and number of errors exceeds a certain pre- 
scribed maximum, no credit is allowed. The score of any 
child is ascertained by adding together all the credits which 
he has earned on the several paragraphs. This process be- 
comes much more simple than it sounds here when explicit 
directions and the detailed data for each child and for tabu- 
lating results are at hand. 

Silent reading versus oral reading. Notwithstanding the 
fact that oral reading has received much greater emphasis in 
our schools than silent reading, the latter is far more impor- 
tant. Silent reading is required in practically all of the other 
school subjects. Also the pupil will read silently much more 
frequently than orally after he leaves school. However, at 
first oral reading is a means for teaching silent reading. 
Hence in the primary grades it is worth while to measure 
the ability of pupils to read orally. 

Summary. In this chapter we have described two silent 
reading tests, one vocabulary test and one test for oral read- 
ing. The detailed instructions for using these tests have not 
been reproduced since they always are furnished with the 
tests. We have given only those general directions which 
were considered necessary for understanding the tests and 
the scores obtained by using them. Certain words which are 
used in discussing educational tests have been introduced. 
The reader should study the meaning of these words care- 
fully because they will be used frequently in the following 



42 MEASURING THE RESULTS OF TEACHING 

chapters. The most important of these words are: score, 
distribution of scores, central tendency, median, class scores. 
In the next chapter we shall consider the meaning or inter- 
pretation of scores and how to correct the defects revealed 
by the tests. 

QUESTIONS AND TOPICS FOR STUDY 

1. What is silent reading? What is oral reading? Which is the more 
important? Why? 

2. What are the essential features of Monroe's Standardized Silent 
Reading Tests? 

3. What are the essential features of Courtis's Silent Reading Test 
No. 2? 

4. What is a distribution of scores? 

5. What is the median score? 

6. How is the median score found in using Monroe's Standardized 
Silent Reading Tests? 

7. Why should a vocabulary test be used? 

8. Have you been satisfied with your marking of pupils in reading? 
How have you tested pupils in reading? Do you think you have done 
it as well as you could by using the tests described in this chapter? 

9. Have you been placing too much emphasis upon oral reading? How 
could you find out? 



CHAPTER III 

THE MEANING OF SCORES AND CORRECTING DEFECTS 
IN READING 

I. Monroe's Standardized Silent Reading Tests 

Standards necessary to give scores meaning. Seven 
seventh-grade pupils made the scores in Table V when given 
Monroe's Standardized Silent Reading Test in April. Al- 
though it is obvious that certain of these scores are larger 
than others none of them mean very much until we know 
what scores a seventh-grade pupil should make. That is, 
standard scores are necessary for interpreting the scores of 
pupils or classes. 

Table V. Showing Scores of Seven Seventh-Grade Pupdls on 
Monroe's Standardized Silent Reading Test. 



Pupil 


Comprehension score 


Rate score 


A.N. 


35.0 


146 


E.A. 


27.6 


98 


C.S. 


23.1 


146 


H.H. 


22.8 


146 


R.H. 


17.8 


85 


F.S. 


14.5 


54 


E.P. 


11.8 


98 



These tests have been given to several thousand pupils in 
each grade and the resulting scores tabulated as the scores 
of a class are recorded. (See form on page 28.) From these 
distributions it is a simple matter to calculate the scores 
which the "average" or typical pupil in each of the grades 
makes. These scores are standard scores. Table VI gives the 
standard May scores for these tests; that is, the scores which 
the "average" pupils completing the respective grades 
make. When the tests are given at the beginning of the 



44 MEASURING THE RESULTS OF TEACHING 

school year, one would use the standards of the grade below 
for judging the pupils' scores. In case the tests are given at 
some time during the school year, say at the end of the 
fourth month, approximate standard scores for this date 
can be calculated from the facts of Table VI. 

Table VI. Standard May Scores for Monroe's Standardized 
Silent Reading Tests 

Test I Test II 

Grade Ill IV V VI VII VIII 

Comprehension 9.0 14.5 21.0 21.0 24.0 27.5 

Rate 60 80 93 92 102 108 

The seventh-grade scores in Table V were obtained by 
giving the tests April 15 which is about the end of the eighth 
month of school, but since the difference between the sixth- 
and seventh-grade standards is not large, we can use the 
May standards without introducing an appreciable error. 
Pupil A. N. (scores 35.0, 146) is distinctly above standard 
in silent reading ability as shown by this test. Pupil E. A. 
(scores 27.6, 98) is above in comprehension, but slightly be- 
low in rate of reading. Pupils C. S. and H. H. (scores 23.1, 
146; 22.8, 146) are approximately standard in comprehen- 
sion and read very much faster than the standard rate. The 
other three pupils are below standard in both comprehension 
and rate. Pupil E. P. (scores 11.8, 98) is close to the stand- 
ard in rate, but his comprehension score is less than half of 
the standard. Pupil F. S. (scores 14.5, 54) reads very slowly, 
which makes impossible a high comprehension score — al- 
though he did only two exercises incorrectly. Thus stand- 
ards make it possible for a teacher to give a meaning to each 
score. 

Interpreting scores by graphical representation. Some 
persons grasp the meaning of facts more easily when they 
are represented graphically. These standards and scores 
are easily represented by distances on a straight line as 



CORRECTING DEFECTS IN READING 



45 



shown in Fig. 7. In this figure the standards for Grades 6, 7, 
and 8 are represented by distances on the two horizontal 
lines. In each case the scale has been chosen so that the 
sixth-grade standard for rate (92) is directly under the com- 
prehension standard (21). The same has been done for the 
seventh- and eighth-grade standards. This plan produces an 



Comprehensioriin 6 IV V 




Test I 


3 6 


? ' " /a. " ' / 


*r ' ' 2 


i 


25" 


30 <M 


°*U> ' 1 


>o ' « 


JO ' ' 


33 


IOQ 


/io /4o 



Co mprehension ,e- ft. rs. vl 



TeslH. 




Fig. 7. Showing a Scheme for the Graphical Representation of the 
Scores of Monroe's Standardized Silent Reading Tests. Lower 
Figure shows the Scores of Four Seventh-Grade Pupils. 

irregular scale, but has the advantage that the standards 
for any grade he on a vertical line. In the figure fines have 
been drawn to represent the scores of four pupils given in 
Table V. 

In the case of pupil E. A., for example, a glance at the 
figure tells us that he reads silently with eighth-grade abil- 
ity, but his rate is slightly less than seventh-grade standard. 
Pupil E. R. reads as rapidly, but is conspicuously below 
sixth-grade standard in comprehension. One advantage of 
this plan of graphical representation is that it gives a mean- 
ing to the amount of difference between the score and the 
standard. It means more to say that a pupil is two grades 
below standard than to say his score is 21 when the standard 
is 27.5. 



46 MEASURING THE RESULTS OF TEACHING 

Interpreting class scores. After the scores of the pupils in 
a class have been recorded on the class record sheet, the 
median score of each distribution is found. The median 
scores are the "class scores." (See page 29.) These are in- 
terpreted in the same way as the scores of individual pupils. 
However, one should remember that since the median rep- 
resents the "average" or general status of the group, devia- 
tions from the standards will not be so large as the devia- 
tions of individual scores. Thus a difference of a few units 
between a standard and a median score is much more sig- 
nificant than a similar difference in the case of the scores of 
individual pupils. 

II. Courtis's Silent Reading Test No. 2 
Standards. The standard scores for Courtis's Silent Read- 
ing Test No. 2 are printed on the class record sheet. They 
are reproduced in Table VII. They are to be used in the 
same general way as the standards for Monroe's Standard- 
ized Silent Reading Tests in the interpreting of both indi- 
vidual and class scores. These standards represent the per- 
formance of the "average" or typical pupil in the respective 
grades. The plan of graphical representation described 
above may profitably be used here also. 

i Table VH. Standard Scores for Courtis's Silent Reading 

Test No. 2 

Grade II III IV V VI 

Words per minute 84 113 145 168 191 

Questions in five minutes 16 24 30 37 40 

Index of comprehension 59 78 89 93 95 

Interpreting individual scores. In Folder D, Series R, 
Courtis gives the following suggestions for interpreting 
pupils' scores obtained by using his test. 

Three types of comprehension scores are possible. 

(A) Large negative indices. 

(B) Zero, small positive, or negative indices. 

(C) Large positive indices. 






CORRECTING DEFECTS IN READING 



47 



The general meaning of these is as follows : 

(A) The child misreads. That is, he not only fails to compre- 
hend what he reads, but he persistently gets the opposite 
meaning from that in the sentence. 

(B) The child is guessing at the answers and is not reading 
at all. Repeat the test with appropriate explanations until 
you are sure he understands what is wanted. Then measure 
him again, using a new form of the test. Two forms have 
been printed : The Kitten Who Played May Queen (Form 
I), and The Kitten Who Went to a Picnic (Form II). 
Order by form number. 

(C) All other scores are to be interpreted in the light of the 
relation between rate of reading and the rate of answer- 
ing questions. The general scheme is as follows: 

High and low mean higher or lower than the median score of 
the class. 





Scores 




Interpretation 


Type 


Hate of 
reading 


Rate of 
ansicering 
questions 


Index of 
compre- 
hension 


Probable meaning 


1 
2 


High 


High 


High 


Marked ability. 


High 


High 


Low 


Needs training in accuracy. 


3 


High 


Low 


High 


Defect in mechanical skill offset 
by intelligent re-reading until- 
meaning is comprehended. 


4 
5 


High 


Low 


Low 


Poor training or poor ability. 


Low 


High 


High 


Cautious, careful reading on first 
trial. Such children usually 
make much higher scores on 
second trial. 


6 


Low 


High 


Low 


Marked lack of intelligence. 


7 • 
8 


Low 


Low 


High 


Lack of native ability, but good 
training. 


Low 


Low 


Low 


Lack of native ability, or marked 
defects in training. 



48 MEASURING THE RESULTS OF TEACHING 

Interpreting class scores. To assist one in interpreting 
the class scores of a building or of a school system, Courtis 
has devised the graph sheet shown in Fig. 8. This device 
shows in a very effective way the median scores for " Ques- 
tions answered" and "Index of comprehension" of an entire 



II 

60 
50 
40 
30 
20 
10 



20 



30 



Index of Comprehension 
40 50 60 70 8 



90 



100 



. © 




Fig. 8. Showing graphically the Median Scores of a School in 
Silent Reading as determined by the Courtis Silent Reading 
Test No. 2. (Table VIII.) 

For each class, move a pencil up, but not touching, the scale for questions answered at the 
left of the figure until a point is reached corresponding to the class score for questions an- 
swered. Then move the pencil parallel to the scale for index until a point is reached which 
is directly below the point on the scale corresponding to the index for the class. Finally 
lower the pencil to the paper at this point and make an X. Join each X to the next by a 
straight line. 

In the figure an X has been drawn to represent the scores, 15 questions answered and 
85 per cent index. 



building. The circles through which the dotted line passes 
represent the standard scores. They are joined by the line 
so as to aid one in comparing their position with the position 
of the scores of any class. The directions for drawing this 
graph are reproduced just below the figure. The position of 



CORRECTING DEFECTS IN READING 49 

the X's through which the solid line passes represents the 
scores given in Table VIII. Among the things which this 
figure tells us the most obvious are: (1) The second grade is 
noticeably above standard in "Index of comprehension," 
but slightly below in number of questions answered; (2) the 
sixth grade is above in both abilities, particularly in number 
of questions answered; (3) the third, fourth, and fifth grades 
are near standard; the fifth grade is exactly standard. 

Table VUL The Scores of One School 

Grade II III IV V VI 

Questions answered 16 26 32 36 50 

Index of comprehension 69 76 92 94 98 

III. Thorndike's Visual Vocabulary Scale 

Standards. This scale has not been satisfactorily stand- 
ardized, but we give in Table IX the average score for eight- 
een cities in Indiana 1 and for Louisville, Kentucky. 2 These 
scores are based on the use of another vocabulary scale which 
is supposed to be equal in difficulty to the one described on 
page 36. Thus the facts of Table IX may be used as tenta- 
tive standards for interpreting individual and class scores. 

Table IX. Median Scores in Visual Vocabulary 
(Thorndike Scale A) 

Grade Ill IV V VI VII VIII 

Eighteen Indiana cities 4.00 5.26 6.00 " 6.66 7.29 7.91 
Louisville 4.4 5.3 6.4 7.1 8.2 

IV. Gray's Oral Reading Test 

Standards. The standards for this test are given in Table 
X. It will be noticed that after the third grade the increase 

1 Haggerty, M. E., The Ability to Read : Its Measurement and Some 
Factors Conditioning It. Indiana University Studies, vol. rv, no. 34. 
(January, 1917.) 

2 Race, Henriette V., " The Work of a Psychological Laboratory, Ed- 
ucaiional Administration and Supervision, September, 1917. 



50 MEASURING THE RESULTS OF TEACHING 

in the standards from grade to grade is only one unit, except 
in the seventh, where there is a decrease from the sixth. This 
condition is caused by the particular way in which the scores 
are computed, and does not mean that a pupil reads orally 




Fig. 9. Showing a Scheme for the Graphical Representation of 
Scores on Gray's Oral Reading Test. (After Gray.) 



no better in the eighth grade than he did in the fifth. This 
apparent inconsistency in the scores for the several grades is 
corrected in the plan of graphical representation shown in 
Fig. 9. The vertical line for each grade has a scale which 
begins at a different height. The position of the broken line 
represents the standard scores. This diagram may be used 
for interpreting either individual or class scores. 



CORRECTING DEFECTS IN READING 51 

Table X. Standard Scores for Gray's Oral Reading Test 

Grade I II III IV V VI VTI VIII 

Standard 31 43 46 47 48 49 47 48 

V. Correcting Defects in Silent Reading 

Scores furnish a basis for improving instruction. In order 
that the greatest benefit may be derived from the use of 
standardized tests, it is important that those using them 
understand the purpose of such tests. Their function is to 
f urnish reliable information concerning what pupils are able 
to do in a certain field, such as silent reading or oral reading. 
The mere giving of the tests does not increase the abilities of 
the pupils, but when a teacher knows the abilities of his 
pupils and the standard scores for their grade, he has in- 
formation which will be very helpful in planning future 
instruction. In the following pages we give records of the 
scores of a few typical classes and suggestions for improving 
the conditions represented by these scores. The first three 
illustrate scores obtained by using Monroe's Standardized 
Silent Reading Tests and the next two illustrate scores ob- 
tained by using Courtis's Silent Reading Test No. 2. 

Type I. Below standard in comprehension. The first type 
which we shall consider is that of a class which is conspicu- 
ously below standard in comprehension as shown by Mon- 
roe's Standardized Silent Reading Tests. The scores of such 
a fifth-grade class are shown in Fig. 10. The fifth-grade 
standards are: Rate 93, Comprehension 21.0. The intervals 
in which these standards fall are indicated in Fig. 10. The 
class score for rate is slightly below standard, but this is a 
minor matter compared with the position of the compre- 
hension scores. 

Individual differences. Another very noticeable feature of 
Fig. 10 is that the scores are widely scattered, which means 
that the pupils of this class which have been grouped to- 



52 MEASURING THE RESULTS OF TEACHING 




Fig. 10. Showing the Scores of a Fifth-Grade 
Class on Monroe's Standardized Silent 
Reading Tests. (Type I.) 



gether for instruc- 
tion do not possess 
equal ability in si- 
lent reading. In 
fact they are shown 
to differ very wide- 
ly. This condition 
is not unusual, but 
the pupils of some 
classes are found 
to be more closely 
grouped than others, 
and we may say 
that while it prob- 
ably is not possible 
to eliminate indi- 
vidual differences 
altogether, a close- 
ly grouped set of 
scores is one "ear- 
mark" of good 
teaching. Individ- 
ual differences will 
be considered more 
fully under Type 
III. 

The causes of a 
lack of comprehen- 
sion. The teacher 
of the class whose 
scores are given in 
Fig. 10 faces the 
problem of improv- 
ing their ability to 



CORRECTING DEFECTS IN READING 53 

comprehend. The lack of comprehension may be due to 
one or more of several causes : (l) A lack of a good " method " 
of reading silently. (2) A lack of practice in reading 
silently with care due (a) to insufficient opportunity or 
(b) to the absence of a strong motive. (3) Not sufficiently 
acquainted with the vocabulary. (4) Miscellaneous causes, 
such as becoming confused on the test or failing to under- 
stand what is to be done. If the teacher exercises care 
to follow the directions in giving the test such causes as 
this are unlikely to happen for the entire class and hence 
do not need to be considered in this place. 

Diagnosis, or locating the cause of poor comprehension. 
(a) Vocabulary. In the case of a given class it will be neces- 
sary for the teacher to determine which of the above causes 
apply. He will frequently be able to do this simply by 
reason of his acquaintance with the pupils. If he is 
doubtful, Thorndike's Visual Vocabulary Test may be used 
to determine if the poor comprehension is due to the lack 
of vocabulary, or, if this test is not available, the teacher 
may select a list of words from the exercises read and ask the 
pupils to define them and to use them in sentences. This 
may be done either orally or in writing. 

(b) Method. Evidence of a poor " method " of reading will 
be found in the character of the pupil's responses to the 
exercises. Efficient silent reading involves three steps : (l) as- 
signing to each word or phrase its correct meaning; (2) com- 
bining the several elements of meaning, giving to each its 
proper weight or significance; (3) verifying or comparing 
the meaning (in the case of Monroe's Standardized Silent 
Reading Tests, the answer to the question) with the sen- 
tence or exercise to see if it is the correct meaning. Some 
pupils do not go through these steps. They merely "fish 
around" in the exercise for a word or phrase to use as the 
answer to the question. This is not reading; it is only guess- 



54 MEASURING THE RESULTS OF TEACHING 

ing and not a "method" of reading. Evidence of this pro- 
cedure will be found in the pupil's responses. If they are 
uniformly unreasonable or absurd, it is reasonably certain 
that the pupil is "guessing" or writing down the first thing 
which comes into his mind unless he is very deficient in 
vocabulary. 

An illustration of " guessing " in silent reading. Some- 
times it is wise to secure further evidence. This can be done 
by requiring the pupil to answer questions based upon a 
paragraph such as the following: 1 

In Franklin, attendance upon school is required of every child 
between the ages of seven and fourteen on every day when school 
is in session unless the child is so ill as to be unable to go to school, 
or some person in his house is ill with a contagious disease, or the 
roads are impassable. 

1. What is the general topic of the paragraph? 

2. How many causes are stated which make absence excusable? 

3. What kind of illness may permit a boy to stay away from 
school, even though he is not sick himself? 

4. What condition in a pupil would justify his non-attendance? 



The following answers to the above questions by sixth- 
grade pupils are taken from a report by Thorndike 2 and are 
typical of responses which indicate that the pupil is " guess- 
ing" at the answer to the question, either on the basis of 
what the paragraph or some word in it suggests to him or on 
the basis of his general experience. The number following 

1 This paragraph and the questions are taken from Thorndike's Scale 
Alpha 2, Part II, Set V. This scale may be purchased from the Bureau of 
Publications, Teachers College, New York City. A similar test, arranged 
in a more convenient form for classroom use and called the Minnesota 
Scale Beta, may be secured from the Bureau of Cooperative Research, 
University of Minnesota, Minneapolis, Minnesota. 

2 Journal of Educational Psychology, vol. 8, p. 324, June, 1917. 



CORRECTING DEFECTS IN READING 55 

the answer is the number of times it occurred per hundred 
papers. (Two hundred papers were examined.) 

Question 1. 

Franklin 4 1/2 

Franklin attends to his school 1/2 

It was a great inventor 1/2 

Because it's a great invention 1/2 

Question 2. 

If the child is ill 2 

Illness 1 

Very ill 3 

An excuse 2 

Question 3. 

If Mother is ill 5 1/2 

Headache, ill 1/2 

A sore neck 1/2 

When a baby is sick 1/2 

When the roads cannot be used 1/2 

Question 4 

By bringing a note 6 

To have a certificate from a doctor that the disease is 

all over 1/2 

Torn shoes 1/2 

When he acts as if he is innocent 1/2 

Being good 1/2 

Get up early 1/2 

Come to school 11/2 

If he lost his lessons 1/2 

Truant 1 

If some one at his house has a contagious disease 6 1/2 

Not smart 1/2 

By not staying home or playing hookey 1/2 

An illustration of failure to verify meaning. In some cases 
the answers to questions indicate that the pupils are not 
"guessing," but are inaccurate because they fail to verify 
or compare their answer with the paragraph read. Obviously 
this step was not taken by the pupils who made the answers 



56 MEASURING THE RESULTS OF TEACHING 

quoted above, but they committed another error. They did 
not try to read. They simply "guessed" or took the first 
idea which came into their minds and did not even ask if it 
was sensible or foolish. But such answers as the following 
suggest that the pupil "tried" to read but failed to answer 
correctly, partly because he did not verify his answer: 

^Question 1. 

The attendance of the children 1/2 

School. 7 1/2 

About school 4 

How old a child should be 1/2 

Question 3. 

Serious 1/2 

Contagious disease, roads impassable 1 1/2 

Question 4. 

Somebody else must have a bad disease 1/2 

Illness, lateness, or truancy 1/2 

r Thorndike says: 

Reading may be wrong or inadequate because of failure to treat 
the responses made as provisional and to inspect, welcome, and 
reject them as they appear. Many of the very pupils who gave 
wrong responses to the questions would respond correctly if con- 
fronted with them in the following form: 

Is this foolish or is it not? 

The day when a girl should not go to school is the day when 
school is in session. 

The day when a girl should not go to school is the beginning of 
the term. 
" The day etc is Monday. 

The day is fourteen years. 

The day is age eleven. 

The day is a very bad throat. 

Impassable roads are a kind of illness. 

He cannot pass the ball is a kind of illness. 

They do not, however, of their own accord test their responses 
by thinking out their subtler or more remote implications. Even 



CORRECTING DEFECTS IN READING 57 

very gross violations against common sense are occasionally 



i 

Reason for failure to verify meaning. In another place 
he comments upon the general reason for this: 

There seems to be a strong tendency in human nature to accept 
as satisfactory whatever ideas arise quickly — to trust any course 
of thought that runs along fluently. If the question makes the 
pupil think of anything or if he finds anything in the paragraph 
that seems to belong with the question, he accepts it without criti- 
cism. Wrong answers are, in reading tests with all ages, too fre- 
quent in comparison with admissions of ignorance. This holds of 
tests in other subjects also. 

It seems probable that in scoring pupils' work in schools an 
admission of ignorance should not be penalized as heavily as an 
absurd or specially harmful error, and that inadequacies and errors 
in general should be penalized somewhat more heavily than they 
now are, at least in the many cases where it is much more useful 
to know that one does not know and to say so, than to respond 
wrongly. On the other hand, a mere chronic suspicion and skep- 
ticism concerning one's ideas is undesirable. It is healthy to trust 
the ideas which the laws of habit produce, provided we maintain 
an active watch for other ideas which may tell whether the first 
ones are appropriate. The pupil should learn to criticize his re- 
sponses, but not to be frightened into a mental paralysis. 2 

An illustration of the lack of vocabulary. The lack of 
vocabulary is indicated by such responses to the first ques- 
tion of the exercise on page 54 as the following: 

Question 1. Per cents 

A few sentences 1/2 

Made of complete sentences 1/2 

A sentence that made sense 1/2 

Subject and predicate. 1/2 

A letter 1/2 

Capital 5 1/2 

1 Journal of Educational Psychology (June, 1917), p. 330. 

2 Elementary School Journal (October, 1917), vol. 18, p. 107. 



58 MEASURING THE RESULTS OF TEACHING 

Per cents 

A capital letter 1/2 

The first word 1/2 

Leave half an inch space 2 1/2 

The heading 1/2 

Period 1/2 

An inch and a half 1/2 

An inch and a half capital letter 1/2 

How to correct such defects, i. Motivation. Pupils who 
are "reading" in the ways described on the preceding pages 
must, first, be caused to desire to read better, that is, their 
silent reading must be motivated more strongly; second, they 
must be given practice in careful reading by the teacher 
making use of and creating situations in which emphasis is 
upon thought-getting and not upon oral expression or rate 
of reading. 

Silent reading motivated by the use of standardized tests. It 
has been the experience of many teachers who have used 
standardized tests that a strong motive is frequently created 
by telling the pupils the standards for their grade and the 
scores of their class. This gives the pupils a definite aim to 
work for and a statement of the progress which the class 
must make. It secures for the teacher the cooperation of 
the class, which is very important. The writer has visitea 
classrooms where the teacher had the class scores and the 
standards represented graphically on a chart which was 
posted in the front of the room. If the class was below stand- 
ard, the pupils were interested in having the class scores 
brought up to standard. 

Commendable results have also been secured by having 
each pupil compare his scores with the standards. This 
stimulates the pupil to compete with an objective standard 
and not with his classmates. Thus the undesirable feature of 
competition is eliminated. If the tests are repeated from 
time to time, the pupil also has the advantage of comparing 



CORRECTING DEFECTS IN READING 59 

his successive scores. He thus learns the amount of his 
progress. The teacher should bear in mind that probably 
all pupils will not attain the standards and that some will 
exceed them. A pupil who is below standard, but is making 
progress, may be doing all that is possible for him in the 
time that is devoted to reading. If he is, the teacher must 
make certain that he does not become discouraged. 

2. Emphasis upon thought-getting, (a) In the 'primary 
grades. Children in the primary grades should from the start 
have exercises in which the meaning is the only significant 
element, and the response is not in terms of words said, but 
things done, or interpretations made. For example, let it 
be the usual thing for the child to carry out the directions 
contained in the word or sentence. The primary teacher 
should be supplied with some hundreds of cards upon which 
such sentences or short paragraphs as the following are 
printed or written: 

(1) Draw a picture of a flag on the blackboard. 

(2) Make a sound like a cross kitty makes when a dog chases her. 

(3) Hide behind the door. 

(4) Play that you are carrying a cup full of water and do not 
wish to spill any of it. 

These cards should be graded in such a way that certain 
ones will contain only the words taught in the first reading 
lessons. As more words are learned, more cards will become 
available. Variety in handling the exercises may be intro- 
duced in scores of ways which will readily occur to a re- 
sourceful primary teacher. Many other devices having the 
same aim will also occur to the teacher. The essential thing 
is that practice in translating written or printed language 
into action instead of words should be started early, thus 
producing the habit of advancing through a paragraph by 
thought-units rather than by letters, syllables, or words. 

(b) Above the primary grades. In grades above the primary 



60 MEASURING THE RESULTS OF TEACHING 

the problem is fundamentally the same as stated for the 
primary, but the devices must vary. ■ -* 

First, whenever reading is done orally, be sure that what 
the child is reading is new to most of his listeners. Be sure, 
too, that the other pupils are listening, and not following 
along with the reader in another copy of the same book. No 
method of reading is more faulty in intermediate grades 
than that in which other members of the class are watching 
for a word error of the reader, ready to call attention at once 
to such a mechanical mistake. This method centers the at- 
tention of the reader constantly upon the mechanics and 
never develops the habit of attending first to the thought. 
Whereas, if the reader realizes that his hearers know nothing 
of the content of his selection except what they gather from 
his reading, then giving the thought instead of pronouncing 
the words becomes the controlling factor in his conscious- 
ness. It follows from this that only selections, the thoughts 
in which are vital to children, should be used as subject- 
matter for such reading. Then let the one who has read such 
a selection defend the selection against questions or criti- 
cisms of the class. In short, center attention upon the mean- 
ing, even at the expense, if necessary, of accuracy in pro- 
nunciation, enunciation, and expression. 

Second, let the amount of reading which is compellingly 
interesting be increased. Supplementary reading in geog- 
raphy, history, science, and literature should be given a 
larger place. Require that the reports made upon such read- 
ings be rather exact, but let the selections be reasonably easy 
for the children. Gain in facility in silent reading cannot be 
secured by holding the children to selections which are so 
difficult that word-troubles absorb all the attention. One 
must be able to go with ease through the successive 
thoughts before the habit of attending to the thought can 
be acquired. 



CORRECTING DEFECTS IN READING 61 

Third, make all the industrial and playground exercises 
give a far greater measure of service in teaching reading than 
they now commonly give. How singularly short-sighted 
we are to ask a child to follow the directions printed in his 
arithmetic for finding the per cent that one number is of 
another, but employ a teacher to give orally the directions 
for playing a new game, making a raffia basket, or plant- 
ing beans. The very things which come nearest the natural 
interests of the children, concerning which they would most 
zealously read if they had the paragraphs containing the 
needed directions, are given to them orally. When interest- 
ing school exercises require a careful following of directions, 
then those directions make the most effective silent reading 
material. But in practice we seldom make use of them. 
This fault is due to a failure to understand the distinction 
between the aim of the intermediate grades and the aim of 
the upper grades. If we realized that all the work of the 
intermediate grades should be made to develop skill in using 
the tools of learning, then we should not conduct these exer- 
cises without making them aid in teaching reading. 

(c) In the upper grades. Passing now to the situation pre- 
sented when the score of a class above intermediate grades is 
found to be low, we have the most serious task of all. The 
junior high-school or upper-grade pupil should be able to 
proceed with his school tasks without much attention to the 
tools he is using. It is not the primary function of this de- 
partment of the school system to increase the children's fa- 
cility in the handling of these tools. However, success in 
nearly all the tasks undertaken in the upper grades depends 
upon the skill which the children are expected to possess in 
the tool subjects. A compromise is, therefore, necessary, if 
children in the junior high school or seventh and eighth 
grades, are found deficient in their ability to read silently. 
A few suggestions are here offered in the hope that some help 



62 MEASURING THE RESULTS OF TEACHING 

may come from them, although it is realized that correcting 
reading faults at this stage is very difficult. • 

First of all, the children's own conscious efforts should be 
obtained in the direction of correcting the faults. Then, too, 
the teacher should see that he is observing the same funda- 
mental principles stated for the intermediate grades. Com- 
prehension, and not mechanics, must be made the test of all 
reading, whether in history, science, or literature. The ma- 
terial selected for use must be sufficiently easy so that the 
children are not tied up in word or language difficulties. 
Again, to overcome the habit of proceeding by too small 
units, practice must be afforded in advancing by short sen- 
tences or phrases. 

In case the trouble seems to be that the children read 
fluently enough orally, but get little of the thought, intro- 
duce a great deal of the sort of reading requiring close atten- 
tion to the thought. For example, use rule books for foot- 
ball, basket-ball, and the like for those interested in games; 
catalogue descriptions; directions for making certain 
stitches; the more involved arithmetic problems; and so on. 
These things possess a minimum of word-difficulty and a 
maximum of thought-difficulty. They require the imagina- 
tion to construct a picture little by little and hold it up for 
constant modification as the reading proceeds. Thus, atten- 
tion is focused on thought. 

Where the class appears to have the right habits of reading 
silently, but have had insufficient practice, the obvious sug- 
gestion is to give them all the practice possible. Much sup- 
plementary reading upon which they make only meager 
reports, if any , will help. Try to secure as much general Lome 
reading as possible. See that an abundance of interesting 
things is available for reading, and stimulate interest by hav- 
ing the children's criticisms of them given before the class. 

3. Exercises requiring careful reading to answer ques- 



CORRECTING DEFECTS IN READING 63 

tions. Exercises of the kind shown on page 54 can be used 
to an advantage in teaching pupils to comprehend what they 
read. Exercises may be taken from the tests mentioned in 
the footnote, but a teacher will not find it difficult to con- 
struct similar exercises by asking a series of questions based 
upon paragraphs in the pupils' geography, history, or other 
texts. If supplementary readers are available, they can also 
be used in this way. The teacher can write the questions on 
the board or dictate them. The next day the papers should 
be returned and the attention of the pupils called to their 
errors. This plan can be varied by having the pupils turn 
to a particular paragraph in their text and prepare an ap- 
propriate set of questions on it. The teacher can judge the 
questions upon the basis of whether they call for the impor- 
tant ideas in the paragraph. 

The use of such exercises does two things : first, answering 
the questions will give the pupils an idea of what careful 
reading involves; second, their attention will be directed to 
the necessity of verifying their answers. 

4. More attention to vocabulary. If the cause is found to 
be a lack of acquaintance with the meaning of the words 
used, more attention should be given to vocabulary. In the 
upper grades the use of the dictionary will help, but the 
most important thing is that the teacher shall definitely 
recognize the necessity for teaching the meaning of words, 
net merely formal dictionary definitions, but rich, compre- 
hensive meanings which are directly connected with the ex- 
periences of pupils. It is frequently worth while to spend 
five or ten minutes in a class discussion of the meaning of 
an important word. The use of a vocabulary test will tend to 
direct the attention of the teacher to the necessity for doing 
this. It may also happen that when the pupil finds that he 
is below standard in vocabulary his cooperation will be 
secured. 



64 MEASURING THE RESULTS OF TEACHING 



Rate Score j 


Comprehension Score 


Interval 


Number 

of 
Pupils 


Interval 


Number 

of 
Pupils 






80 & above 

70 to 79-9 

60 to 69- 9 

50 to 59.9 

45 to 49.9 

40 to 44.9 

35 to 39-9 

30 to 34.9 

27 to 29.9 

24 to 26-9 

21 to 23.9 

18 to 20-9 

15 to 17.9 

13 to 14.9 

11 to 12.9 

9 to 10-9 

7 to 8-9 

5 to 6.9 

4 to 4.9 

3 to 3.9 

2 to 2.9 

1 to 1.9 

to .9 




12C to 130 
121 to 125 









116 to 120 




111 to 115 


Ill 


106 to 110 




101 to 105 





96 to 100 




91 to 95 





86 to 90 




81 to 85 


? 




76 to 80 






71 to 75 






66 to 70 


.....3. 

ZIZ 
....£:..... 




61 to 65 
56 to 60 


/ 


51 to 55 




46 to 50 




41 to 45 
36 to 40 
31 to 35 
26 to 30 


S 

Ill 


::x: 

JO 

3 .... 
...„#,... 

...A 


21 to 25 


l 


16 to 20 
11 to 15 




6 to 10 




S 

Y'" 


to 5 


i 








Total 


3¥ 


Total 


3f 


Median 


¥3 


Median 


S.1 



Fig. 11. Showing the Scores of a Fourth- 
Grade Class on Monroe's Standardized 
Silent Reading Tests. {Type II.) 



5. Providing op- 
portunity for prac- 
tice in silent read- 
ing. This point will 
be discussed more 
fully under Type 
III, but attention 
should be called to 
this means of im- 
proving the ability 
of pupils to com- 
prehend what they 
read. Reading is 
an art and pupils 
must have much 
practice. Supple- 
mentary reading 
material of the right 
kinds should be pro- 
vided and definite 
provision should be 
made for opportun- 
ity to read it dur- 
ing school hours. 
The teacher should 
look upon supple- 
mentary reading as 
an important school 
activity and one re- 
quiring his supervi- 
sion. 

Summary for 
Type I. Under this 
type we have con- 



CORRECTING DEFECTS IN READING 65 

sidered the case of a class which has a low comprehen- 
sion score. The causes considered for this condition are: 
(1) failure to use a good "method" of reading; (2) alack 
of practice; and (3) insufficient vocabulary. We have sug- 
gested plans for diagnosis or locating the cause and have 
given several typical illustrations of the causes mentioned. 
The methods of correcting these defects have been pre- 
sented under these heads: (1) motivation; (2) emphasis 
upon thought-getting; (3) exercises requiring careful read- 
ing to answer questions; (4) attention to vocabulary; 
(5) providing practice in silent reading. These methods 
will be considered again under Type III as means of cor- 
recting individual defects. 

Type II. Below standard in rate of reading. In Fig. 11 
there is shown the record of a fourth-grade class which reads 
very slowly. The pupils also made low scores on compre- 
hension but this is due in part to their slow rate of reading 
because when Monroe's Standardized Silent Reading Tests 
are used a high comprehension score is impossible for slow 
readers. 

Causes of slow reading. Three causes may be given for a 
situation such as is illustrated in this second type: (1) the 
common belief that in order to read well one must read 
slowly; (2) over-emphasis upon oral reading which results in 
the pupil pronouncing the words to himself when he reads 
silently; (3) failure on the part of the teacher to recognize 
that the rate of reading is important. 

How to increase the rate of silent reading, i. Motivation. 
One effective plan is to furnish a strong motive. This can be 
done by using standardized tests as suggested on page 58. 
Interesting stories or references for supplementary reading 
will often be effective. If a pupil becomes interested in a 
story, either by having had a part of it read to him or by 
having read the first of it himself, he will be anxious to read 



66 MEASURING THE RESULTS OF TEACHING 

the rest of it to "see how it comes out." While the quality 
of the reading should not be neglected, the emphasis should 
be on the rate of reading. In order that this may be done, 
the reading material must be simple. 

2. Emphasizing rate of silent reading by informal testing. 
One reason why pupils read slowly is that the teacher pays 
no attention to the rate of silent reading. In Chapter I we 
pointed out that one defect in our ordinary measurement of 
results was the neglect of the rate of work. The rate of read- 
ing is an important "dimension'" of the ability to read si- 
lently. In many cases a teacher can increase the rate of his 
pupils' reading by simply recognizing it as one "dimension" 
of the ability to read. This can be done by asking the pupils 
to read silently beginning with a certain paragraph in their 
text (school reader, geography, history, or elementary sci- 
ence). At the end of a suitable period, three to five minutes, 
stop them and have them count the number of lines read. 
This number will be a crude measure of the rate of reading. 
This should be a part of the regular instruction in silent 
reading. If the teacher doubts the quality of the reading, it 
can be tested informally by having the pupils answer a set 
of questions based upon the lines read. 

In the survey of the Cleveland Public Schools an informal 
silent reading test was given by having the pupils read si- 
lently in the Jones Readers. After some preliminary testing 
to give the pupils an understanding of what they were to do, 
the teacher read aloud a page to the class, the pupils having 
their books open. When he came to the turning of the page 
the teacher stopped reading and noted the time. The pu- 
pils continued the reading silently. At the end of one min- 
ute they were stopped and the number of lines read were 
counted. The pages used for the test and the average num- 
ber of lines read are given in Table XI. In interpreting the 
average number of lines given in this table, one must remem- 



CORRECTING DEFECTS IN READING 



67 



ber that the material read in the upper grades was more 
difficult and that the lines contained more words. He may 
use these facts as tentative standards for judging his pupils 
when testing their rate of reading in the way suggested. 

Table XI.* Showing Rate of Silent Reading in Informal 
Testing 













Average number 


Grade 


Book 


Prel 


iminary page 


Test pages 


of lines read — 
44 schools 


2A 


II 




101 


102-103 


16 


3A 


III 




97 


98- 99 


22 


4A 


IV 




61 


62- 63 


21 


5A 


V 




47 


48- 49 


20 


6A 


VI 




63 


64- 66 


24 


7A 


VII 




63 


64- 66 


21 


8A 


VIII 




247 


248-249 


21 


* Judd, C. H., 


" Measuring the Work of the Public Schools," 


Cleveland Education 


Survey, p. 261. 













Rapid readers good readers. It has commonly been 
thought that a thorough understanding required that the 
pupil should read slowly and carefully, and that the rapid 
reader understood very little of what he read. It is, of 
course, true that the pupil who reads with extreme rapidity, 
or "skims" over the page, does not comprehend completely 
what he reads, but we now have evidence which shows that 
in many cases a rapid reader is a "good" reader and a slow 
reader is a "poor" reader. 

Fig. 12 is reproduced from the Report of the Cleveland 
Survey to show the relation which was found to exist between 
rate and quality of silent reading as measured by Gray's Si- 
lent Reading Tests. 1 On the basis of their scores 1831 pupils 
were divided into the nine groups indicated in the figure. 

1 These tests are not described in this book because they are not suited to 
general classroom use. For a complete description of them the reader is 
referred to Gray, William S., Studies in Elementary School Reading Through 
Standardized Tests. (Supplementary Educational Monographs, University 
of Chicago Press.) 



68 MEASURING THE RESULTS OF TEACHING 

The per cent of the pupils in each group is given by the 
number inside of the circle. The size of the circle represents 
the size of the group. The figure shows very clearly that 





Rapid speed and 
good quality 




12 



Rapid speed and 
medium quality 







Rapid speed and 
poor quality 





Medium speed 
and good quality 




Mediumspeed and 
medium quality 




13 



Medium speed 
and poor quality 



O 



Slow speed and • 
good quality 




Slow speed and 
medium quality 



o 



Slow speed and. 
poor quality 



Fig. 12. Per cent of 1831 Cleveland Pupils found in each 
on Nine Speed and Quality Groups in Silent Reading. , 
(From Judd's *' Measuring the Work of the Public Schools.") 

a rapid reader is good in quality more frequently than he is 
poor in quality and the opposite is true for slow readers. 
The application of this fact is that in many cases pupils will 
improve in quality of reading when they increase their rate. 
Teachers should not expect to secure a higher degree of 
comprehension by urging their pupils to read more slowly. 
3. More opportunity for silent reading. Practice in read- 
ing is even more necessary for producing the ability to read 



CORRECTING DEFECTS IN READING 69 

rapidly than for engendering the ability to comprehend. The 
suggestions on page 64 apply here also. It is particularly 
important that the material should not be difficult to 
understand. 

4. Less emphasis upon oral reading in the intermediate 
and grammar grades. Oral reading is necessary in the prim- 
ary grades, but as the pupil progresses from grade to grade, 
more emphasis should be placed upon silent reading and 
less upon oral reading. From about the fourth grade silent 
reading should receive the greater emphasis. Failure to do 
this frequently causes the pupil to acquire habits which 
make rapid silent reading impossible. Two cases of slow 
readers due to this cause are described on pages 73 and 
84. 

Summary for Type II. Under this type we have considered 
the case of a class which reads too slowly. The following 
causes were considered: (1) attempt to secure a high degree 
of comprehension by urging the pupils to read more slowly; 

(2) over-emphasis upon oral reading; (3) failure of teacher 
to recognize the rate as important. For increasing the rate 
of silent reading the following correctives were given: (1) 
motivation; (&) greater emphasis upon the rate of reading; 

(3) more opportunity for silent reading; and (4) less em- 
phasis upon oral reading. 

Type III. Scores too widely distributed. In Fig. 13 we 
show the scores of a fifth-grade class whose median scores 
are approximately standard. (The test was given February 
4, and hence it is not to be expected that the class had at- 
tained the seventh-grade May standard.) The noticeable 
thing about this record is that the scores for rate range from 
one score between 31 and 35 to one above 130, and for 
comprehension from one score between 1 and 2.9 to one be- 
tween 35 to 39.9. Thus, there are in this fifth-grade class 
some pupils below third-grade standards (60, 9.0) and others 



70 MEASURING THE RESULTS OF TEACHING 



RaJe. Score 


Comprehension Score 


Interval . 


Nac&ber 

ai 
PcdUb 


Interval 


number 
.Pupils 


Above 130 


/ 

'/ 


80 & above 

70 to 79-9 

60 to 69- 9 

50 to 59. 9 

45 to 49-9 

40 to 44.9 

35 to 39.9 

30 to 34-9 

27 to 29.9 

24 to 26.9 

21 to 23.9 

18 to 20.9 

15 to 17- 9 

13 to 14-9 

11 to 12-9 

9 to 10.9 

7 to 8.9 

5 to 6.9 

4 to 4.9 

3 to 39 

2 to 29 

1 to 1.9 

to 9 

Total 




126 to 130 




121 to 125 




116 to 120 


.4. 

HI 

rx:.:' 

....&. 


111 to 115 




106 to 110 




101 to 105 
96 to 100 
91 to 95 
86 to 90 


""*" * 


81 to 85 


/ 


76 to 80 




...A 


71 to 75 


::x: 


66 to 70 


/ 


61 to 65 


.Mr 


56 to 60 


::fc: 


51 to 55 




46 to 50 




41 to 45 


£ 


....#. 


36 to 40 




31 to 35 
26 to 30 


/ 


21 to "25 




16 to 20 






11 to 15 


/ 


6 to 10 





to 5 








Tctal 


_££_ 

fd 


Median 


Median 



Fig. 13. Showing the Scores of a Fifth- 
Grade Class on Monroe's Standardized 
Silent Reading Tests. (Type III.) 



above the eighth- 
grade 1 standards 
(108, 27.5). The 
teacher's particular 
problem in this case 
is with the pupils 
who have the low 
scores. Those who 
are above standard 
do not constitute 
a problem, if they 
are above in both 
rate and comprehen- 
sion, except that the 
teacher should con- 
sider whether these 
pupils could spend 
the time now de- 
voted to reading 
more profitably on 
some other subject. 
It might happen, 
for example, that 
some of these pu- 
pils might be below 
standard in arith- 
metic, spelling, or 

1 Accurate comparison 
of fifth-grade scores with 
eighth-grade standards 
is not possible because 
different tests are used 
in these grades. How- 
ever, the statement is 
probably true. 



CORRECTING DEFECTS IN READING 71 

language. If so they need to devote some extra time to 
these subjects. 

The condition shown in Fig. 13 may be due to an unwise 
classification of the pupils and some adjustments should be 
made which would reduce the wide range of scores. How- 
ever, this would probably reduce the number of cases only 
slightly and the problem would still remain. 

Uniformity in instruction for all the members of a class 
widens variability among them, making the weak ones rela- 
tively weaker and the strong ones relatively stronger. To 
prevent this widening of the variability more attention must 
be given to individual instruction. This does not mean a 
leveling of all members of a class, but rather affording a 
maximum of opportunity to each member to do those things 
most needful to him. Those things which he can already do 
well he should not be required to do, even though some other 
members of the class need to do them. 

Those children falling far below the median of the class 
should be given special physical examination to discover if 
possible the cause. Sometimes eyesight is found to be poor. 
Frequently some other physical defect has prevented normal 
mental growth. Sometimes an examination by means of 
approved intelligence tests, such as the Binet-Simon tests, 1 
reveals that the child is mentally incapable of doing work 
of the regular school type. 

Illustrations of individual defects. It may be that the pu- 
pil needs to be taught how to read silently. Not very much 
attention is given to teaching pupils how to read silently. 
The instruction in reading is confined largely to oral reading. 
A pupil who has not learned how to read silently needs in- 
struction. One teacher writes of a certain pupil as follows: 

1 See especially Terman, L. M., The Measurement of Intelligence 
(Houghton Mifflin Company, Boston, 1916). A simple guide for the use 
of the intelligence scale. 



72 MEASURING THE RESULTS OF TEACHING 

From the tests given and from her work in English which I have 
had for two years, I find that she has only a vague hazy kind of 
meaning for many of the words needed for seventh-grade work. 
She does not see words in their relation to others in the sentence. 
When she finds a name for a combination of letters she is satisfied, 
thinking that she is reading. She has failed this year. I hope this 
may rouse her to the effort of which I am sure she is capable. If I 
can only make her see that reading means more than naming words 
and persuade her to work, I am sure she can overcome her diffi- 
culties. 

Another difficulty may be vocabulary. A boy who made 
a low score on the silent reading test was given the vocabu- 
lary test, on which he made a very low score. His teacher 
describes him as follows : 

His greatest difficulty seems to be a lack of vocabulary. He 
memorizes history instead of studying for the thought. Lately, he 
has gotten away from this to some extent and begins to sum up the 
thought rather than repeat words when called upon. He still (after 
some individual instruction) finds so many unfamiliar words in any 
new paragraph that his progress is very slow, but he attacks his 
problem with more intelligence than he showed at first. 

How to bring individual pupils up to standard. If the 
child is nearly normal physically and mentally, but has not 
developed ability to get meaning from printed language, he 
presents a problem in instruction calling for the best profes- 
sional skill to solve. In dealing with such pupils the sugges- 
tion given for Types I and II can be used. Giving the pupil 
a strong motive frequently will solve the problem. 

It is quite certain that a pupil far below the median in this 
basic ability has never made use of printed language to se- 
cure help in satisfying his own childish desires. If possible, 
situations must be brought about in which his desires or 
plans depend for their fulfillment upon his reading. It may 
be, for example, that his mother or father has been in the 
habit of reading stories to him. If so, and he can be made to 



CORRECTING DEFECTS IN READING 73 

be keenly interested in a story by having a part of it read 
to him, he should have to read the rest himself to satisfy his 
desire to know the rest of the story. Possibly he would like 
to be the leader in an occasional nature-study excursion, 
but, of course, it will be expected that he look up informa- 
tion concerning the things they see on the trip and be able 
to report later to the group. That is the business of the 
leader. Or he might umpire the baseball game if he made 
sure of the rules; or assign the parts in the coming school 
entertainment, if he read the various parts carefully so as to 
be able to make a wise assignment; or score the class com- 
positions on the basis of which was most interesting. Such 
a list of possible opportunities for calling into service a 
child's silent reading ability might be largely extended. 
The two things to guard against are (1) making reading a 
punishment and (2) confusing child need with school need. 
The thing to be accomplished is to give the child a chance 
to do something which he really wishes to do, but cannot do 
without reading. 

The case of a slow and inefficient reader. Judd 1 gives the 
case of a girl in the fifth grade who was average or above in 
all her school subjects except reading. In this one subject 
she had been rated as a poor student from the first through 
the fourth grade. Her health was good and she had been 
regular in her attendance at school. With respect to reading 
she is described as follows : 

Reading seems to be her greatest weakness. Her fourth-grade 
teacher reported her as "a slow reader who reads hesitatingly and 
haltingly, repeating words and phrases. Her breathing is very 
shallow, often causing her to pause for breath in the middle of a 
word or phrase. Her voice is thick, heavy, and unpleasantly nasal. 

1 Judd, C. H., Reading: Its Nature and Development. Supplementary 
Educational Monographs (University of Chicago Press), vol.2, no. 4, p. 82. 
(The paragraph headings in this and the other quotations from this mono- 
graph have been inserted by the author.) 



74 MEASURING THE RESULTS OF TEACHING 

Silent reading is particularly distasteful to her. She always settles 
down to it reluctantly and tardily." 

From the home comes much the same story: "She has never read 
a story to herself, though she has several attractively illustrated 
children's books. She frequently, however, after eagerly studying 
the illustrations in a new book, begs to have the story read to her, 
saying, 'You read it, mother. I can't understand it very well when 
I read it myself.' " 

This pupil was carefully tested in both oral and silent 
reading. In oral reading her score was 33, while the standard 
is 48. She made many errors, particularly mispronuncia- 
tions. In silent reading, she read even more slowly than she 
did orally. 

Observations made during the silent-reading tests showed that 
there was much vocalization. The reading was done in a low whis- 
per, and difficult words, as stated above, were spelled out letter by 
letter. She followed the line with her ringer. In one of the early 
practice periods, when urged to read more rapidly, she remon- 
strated, saying that she could not hear the words so well if she did. 1 

The correctives which were used. From the foregoing data 
it is evident that her difficulties in reading were due to a lack of 
familiarity with printed words and a lack of method of working out 
new or unknown word-forms. In an effort to help her overcome this 
handicap she was given various types of training during eighteen 
weeks. The first six weeks were devoted to a great deal of oral 
reading. The second six weeks were spent on drills in phonics and 
in word analysis. During the last six weeks she was given a great 
deal of silent reading. While each period of six weeks thus stressed 
some one phase of reading, all three types of work were carried 
along throughout the eighteen weeks. For example, oral reading 
was continued with less emphasis during the last twelve weeks. 

The selections for oral reading were made along the line of the 
pupil's school interests in history and geography. These included 
Baldwin's Fifty Famous Stories and Thirty More Famous Stories* 
Harding's Story of Europe, Allen's Industrial Europe, Carpenter's Eu- 

1 This is the case of a pupil whose defect was probably caused by over- 
emphasis upon oral reading. The pupil had never been taught to read 
silently. {Author.) 



CORRECTING DEFECTS IN READING 75 

rape, " Our European Cousins Series," the Merrill and the Horace 
Mann Third and Fourth Readers, Tappan's Old World Heroes, 
Terry's The New Liberty, and Brown's English History Stories. 

Phonics and word analysis were emphasized during the second 
six weeks. Various systems of phonics with some modifications to 
suit the particular needs were used. Words mispronounced in oral- 
reading lessons were worked out phoneticalh,', and lists of words 
similarly pronounced were built up and reviewed from time to 
time. There seemed to be a gradual growth in ability to attack an 
unfamiliar word. In the earlier period the pupil frequently looked 
at the word helplessly or pronounced a known syllable, but was 
unable to attack it at all phonetically. She usually asked the in- 
structor to pronounce it. Later she began immediately to sound 
the new word phonetically, and though sometimes making a mis- 
take in the length of the vowel or in the position of the accent, her 
manner of attack indicated that she had confidence in her own 
ability to work it out. 

Silent reading was emphasized during the last six weeks after 
some training in silent reading had been given throughout the first 
twelve weeks. For special training paragraphs or selections dealing 
with topics of particular interest to the pupil were used. In many 
instances the original selections were edited, and the words which 
had been used in the phonic exercises were woven into the text. 
Frequently before the silent reading began a question was raised, 
the answer to which was to be found in the text. Oral or written 
reproduction or a discussion of the thought of the selection usually 
followed the reading. It is interesting to note, in passing, that 
though no effort was made to reduce the vocalization so perceptible 
at first, it entirely disappeared except when an unusually difficult 
passage was encountered. 

The result. One of the significant results is that men- 
tioned in the closing sentence of the above paragraph. The 
pupil had learned how to read silently without pronouncing 
the words in a whisper. After the correctives described 
above had been used, the pupil was tested again in both oral 
and silent reading. She showed a decided gain in rate of oral 
reading and a reduction in the number of errors. In silent 
reading her rate had increased so that she now read more 



76 MEASURING THE RESULTS OF TEACHING 

rapidly silently than orally, whereas before this special 
training the opposite was true. At the same time she made 
large gains in comprehension. 

Her teachers report that Case G [the pupil described above] 
reads with much greater ease and fluency of expression. The 
quality of her voice has improved and the nasal tones have al- 
most disappeared. She seems to enjoy reading silently much more 
than before training. Frequently she expresses a preference for 
reading a passage silently, saying, "I can do it faster." 

The case of a pupil deficient in vocabulary. A seventh- 
grade boy is described by Judd, 1 whose most striking defect 
in reading was a lack of word meaning. He is described as 
follows: 

In general school standing he is rated as a poor student, although 
he is given a grade of good (B) in the manual arts, music, and phys- 
ical training. In all other subjects he is poor. During the past two 
and a half years he has received no grade higher than C in history, 
geography, science, literature, composition, and grammar. In this 
connection it is interesting to note that progress in these subjects 
after the fourth grade is dependent to a large degree on ability to 
get thought from the printed page. 

His teachers report him as a shy, timid boy, easily embarrassed, 
lacking in self-confidence and initiative in the classroom, though 
very energetic and responsive on the athletic field. He rarely takes 
part voluntarily in class discussions, and when called on to do so 
responds in a few brief, fragmentary sentences, badly expressed, 
but usually containing a thought or an idea on the topic being con- 
sidered. His English teacher finds great difficulty in getting him 
to read with any degree of expression, for he makes no attempt to 
group words into thought units. He reads in a dull, monotonous 
tone, slurring words and phrases. When asked to tell what he has 
read, he reproduces a few ideas in short, scrappy sentences, for 
apparently he makes few associations as he reads. His teachers in 
history and geography explain his poor standing in their subjects 
as attributable to an inability to get ideas from the text. He ap- 
parently reads as rapidly silently as any in the class, but gets and 
retains less of the thought. 

1 Judd, C. H., Reading : Its Nature and Development. Supplementary 
Educational Monographs (University of Chicago Press), vol. 2, no 4, p. 106. 



CORRECTING DEFECTS IN READING 77 

The tests in oral and silent reading sustained the opinions given 
by his teachers. In the oral test he read fairly rapidly, pronouncing 
the words mechanically and enunciating poorly. . . . 

The test in silent reading defined more clearly his apparent diffi- 
culties. . . . Clearly this particular seventh-grade boy ranks in 
comprehension at a lower level than the poorest readers in the two 
preceding grades. This result verifies the estimates of his teachers 
of history and geography. 

A resume of the facts brought out by the tests would seem to 
indicate that he has acquired a mastery of the rudimentary me- 
chanics of word recognition, but lagged far behind in the mastery 
of word meaning. He read words as mere names and not as sym- 
bols of ideas. 

The correctives which were used. How to build up a back- 
ground of meaning that would form a basis for his reading was and 
still is an urgent and difficult problem. Because of his interest in 
animal stories and tales of camp and pioneer life, emphasis was laid 
throughout the eighteen weeks on literature dealing with these 
topics. The Boy Scouts' Manual, Custer's Boots and Saddles, Roose- 
velt's Winning of the West, Southworth's Builders of Our Country, 
Book H, the Merrill and the Horace Mann Fourth and Fifth Read- 
ers, Muir's Stickeen, Coffin's Boys of '76, the Seton Thompson 
and Kipling stories, and similar literature were drawn upon freely. 
Silent reading was continued throughout the eighteen weeks, but 
was especially emphasized during the first six weeks and again 
during the last six weeks. After reading a selection the pupil re- 
produced it orally or in writing. These reproductions at first were 
so meager and inadequate that he frequently had to re-read several 
items before he could answer the questions raised. Many selections 
were read in this way paragraph by paragraph, and the main points 
jotted down to assist in the organization of the thought. 

Before the work had progressed very far it became apparent 
that definite word-study was necessary in order to build up a back- 
ground of meaning. Words were studied in the context for mean- 
ing, and certain ones were chosen for detailed analysis of prefix, 
suffix, and stem. A stem-word analyzed in this manner became the 
nucleus for grouping together other closely related words more or 
less familiar to the student. The word "traction," encountered 
in an article on the "Lincoln Highway," brought out a discussion 
of traction engines, their use in plowing, road-building, and trench 
warfare, why so called, etc. This centered attention upon the stem 



78 MEASURING THE RESULTS OF TEACHING 

"tract." As its meaning became clear the following list was 
elaborated : 



subtract 


distract 


attraction 


contract 


extract 


distraction 


detract 


retract 


subtraction 


attract 


contraction 


extraction 



A study of the prefixes in these words gave a point of leverage 
for attacking the meaning of words containing them. In this type 
of prefix study only those words were listed whose stems were 
familiar to the pupil; as, for example: 



recall 


rebound 


retake 


reclaim 


retain 


reinforce 


rearrange 


reform 


return 


regain 


remake 


reframe, etc. 



. In a similar manner an acquaintance was made with the most 
common suffixes. 

The meaning of some words was approached by the study of 
synonyms and equivalent idiomatic phrases. These were, as far as 
possible, studied in the context and discussed at length to bring out 
shades of difference in meaning. "An indomitable hero," met in 
the pioneer tales, brought forth the following synonyms and idio- 
matic phrases: 



indomitable 


fearless 


stout-hearted 


brave 


heroic 


intrepid 


courageous 


bold 


audacious 


resolute 


daring 


defiant 


manly 


plucky 


undismayed 



to look danger in the face 

to screw one's courage to the sticking-point 

to take the bull by the horns 

to beard the lion in his den 

to put on a bold front 

This type of intensive word-study was continued throughout 
the first six weeks, but was supplemented by incidental word-study 
during the remaining twelve weeks. 

Oral reading was given special attention during the second six 
weeks and continued during the following six weeks. The literature 



CORRECTING DEFECTS IN READING 79 

was of the same general type as that used in silent reading. The 
purpose was to improve, if possible, enunciation and expression. 
Special drills in the enunciation of vowels and of the terminal and 
initial consonants were a part of each reading lesson. Many of 
these drills were taken from reading books. Selections were studied 
silently before being read aloud and the meaning discussed. The 
various thought units were marked off and the whole selection was 
then read aloud. Before the close of each lesson the pupil read a 
selection at sight, unaided by this kind of preparation. 

The result. A test in oral reading after this special train- 
ing showed a reduction of fifty per cent in the number of 
errors and a gain in rate of reading. In silent reading a 
greater gain was made, especially in comprehension. 

An illustration of group and individual instruction. A 
fourth-grade teacher 1 has written of her experience in 
teaching reading to a class of twenty pupils by group and 
individual instruction based upon the results of testing. 
Her report is so suggestive that we quote at some length : 

In October pupils were tested to ascertain the oral- and silent- 
reading rate of each individual. Five oral and five silent trials were 
made, and the averages obtained and used as measures of reading 
rate. . . . With but one exception the rapid readers made fewer mis- 
takes. Comprehension was tested informally. Rapidity and com- 
prehension seemed to go together. Intensive instruction was given. 
Especial attention was paid to poor readers. After two weeks 
there was no improvement in the rate of the three poorest readers. 
The only noticeable improvement was made by the better readers. 
It was evident that the least capable were getting the least from 
instruction, though receiving more attention. This presented a 
problem .... 

Ten types of instruction were planned to cover as many indi- 
vidual needs. The class Reader was supplemented by a carefully 
selected list of books for extensive reading. Methods were devised 
whereby maximum effort would be called forth and interest sus- 
tained. Rate was found to be a measure of improvement which the 

1 Zirbes, Laura, "Diagnostic Measurement as a Basis for Procedure"; 
in Elementary School Journal (March, 1918), vol. 18, pp. 505-22. 






80 MEASURING THE RESULTS OF TEACHING 

children could comprehend. They were, therefore, made aware of 
their rate of reading and kept graphic records of their individual 
standings in monthly regrouping tests. "A" readers were those 
whose rate was more than thirteen lines per minute. They were 
given the privilege of selecting their own material from the supple- 
mentary bookshelf for silent reading. This shelf was called "Story 
Row." The books were arranged in groups according to content. 
A regular library system was used so that the teacher could ascer- 
tain at any time what each child was reading and what he had fin- 
ished. The quality of the silent reading could thus be revealed by 
conversation with the pupil. Children who had enjoyed a book 
were asked to review it for others who might care to read it. Fa- 
vorite chapters were illustrated. Some children chose informational 
material. They would recount interesting things which they had 
learned from their reading, and create a great demand for the book 
which they had read. No more than two books could be used by a 
pupil at one time and stories had to be finished before another 
story book could be begun. 

"B" readers were those whose rate was more than nine lines per 
minute, but not more than thirteen. Pamphlets were provided for 
their supplementary reading. The material was easier and the con- 
tent quite suited to their comprehension. Otherwise the system 
used for the "B" readers was like that for the "A" groups. They 
had less time for supplementary reading as they required more in- 
tensive work with the teacher. Their pamphlets were very popular 
and were often read by "A" readers. 

There was also a group called "C" readers whose rate was be- 
tween six and nine lines per minute, and another group of "D" 
readers who read even more slowly and got practically no meaning 
from the subject-matter. Their supplementary material consisted 
of separate stories. These they read with the teacher, alternating 
with her. They liked to have stories read to them. The teacher 
used her book. The group looked over her shoulder and kept the 
place, picking up the story and reading on when she stopped, until 
the end of a paragraph was reached. The meaning was then dis- 
cussed and the reading continued. 

Each child in the class subscribed to a little nature magazine 
which was kept in the desks for reading during odd minutes.. Sev- 
eral other magazines, an atlas, and a file containing good original 
stories by the children were also at their disposal for this purpose. 

The regular reading instruction was the visible means by the 



CORRECTING DEFECTS IN READING 



81 






aid of which each pupil hoped to get into a 
own by the next measurement. 

These groupings were based 
on rate and were not identical 
with those made for corrective 
teaching. The procedures just 
described, together with the in- 
tensive teaching in type lessons 
which follow, were jointly re- 
sponsible for improvements in 
reading rate and quality. This 
report would, therefore, be in- 
complete if detailed descriptions 
of methods used to secure the 
interest of the individual child 
were omitted. [Seven of the 
type lessons relate to oral read- 
ing. They are omitted.] 

Type lesson 3. Silent read- 
ing for the purpose of oral re- 
production and comprehension. 

Type lesson J+. Silent read- 
ing in search of a given phrase, 
answer, idea, or suggestion in 
the content of supplementary 
books, geography text, arith- 
metic text, and blackboard 
work. 

Type lesson 10. Word-study, 
with difficult words, for ready 
recognition, pronunciation, and 
comprehension. Word-building 
and word-structure studied. 



group higher than his 

S i 



S 



a 

a> 



e: 



Results. Fig. 14 shows 
the results for November, 
December, and February in 
silent reading. The range 
of scores has not been re- 
duced. In fact it has been 



e: 

Hi: 



c: 

EH 






Q 






E. 



ffl js 



Et 



W 



w -I 
a ^ 

% 



82 MEASURING THE RESULTS OF TEACHING 

increased, but the significant thing is that the low scores 
have been materially increased in most cases. The letters 
inside the small squares designate the different pupils. 
Pupil T has advanced from two lines a minute to eight lines 
a minute. Pupil R has gone from two lines to twelve lines. 
Pupil S has remained at ten lines. In Fig. 15 we have a 
graphical representation of one of the causes of this prog- 
ress; that is, the average amount of supplementary silent 
reading done during school hours. The increase in the 
amount is very significant. It shows what can be done 
when an effort is made. 

October and Hovsnber 

December and January 



i * i i 1 i i i i i i'i i i i i ■ » " * 

o 20 40 eo 80 KK> 200 300 

Fig. 15. Average Number op Pages of Silent Reading per Pupil 
during School Hours. Supplementary Material. (After Zirbes.) 

Summary for Type HI. When the scores of a class are 
widely distributed, individual instruction is required. Sev- 
eral illustrations of individual defects, the method of dealing 
with them, and the results have been given. One case of 
group instruction supplemented by individual instruction 
has been described. 

Type IV. Slow readers and poor in comprehension in pri- 
mary grades. The class record sheet of a second-grade class 
which was given the Courtis Silent Reading Test No. 3 is 
shown in Fig. 16. It is obvious that the pupils of this class 
both read very slowly and comprehend little of what they 
read. 

The cause: over-emphasis on oral reading. The com- 
monest of all reasons for this situation, particularly when 



CORRECTING DEFECTS IN READING 



83 



found in the grades below the sixth, is that the teachers 
have been placing chief stress upon oral reading. Where 
children are required to give their attention mainly to the 
correct pronunciation of words, the correct enunciation of 
sounds, and the correct inflection of the voice in passing 

[ndex of Comprehension. 



Tablet 
Rate of Reading 


Bcann 

voids em 

ana 


JTOHBOtOF 

CHILD i£H 

EACH 

scou. 




Over 






— 406 






330 






360" 






340 






" 320 






-360 ' 






380' 






" 360 






340" 






: 320" 






300" 






280 






^260 ' 




| 


240 






220 






200 _ 






_ 180 






160 " 






' 140 






120 " 






-106 " 






■" 80 


3 




"60 ' 


1 




40 


S 




20 


r 




" 6 


i 




Total 


i* 




ftbdiaa 


HS- 


i 



DUfnotI* 






Comprd 








kmtm 


M 


Lea 

-5 


-5 to 
+5 


6-39 


10-69 


70-79 


90-54 


85-89 


90-84 


95-99 


100 




70 


























65 


























60 


























55 


























50 


























45 


























40 


























35 


























30 


























25 


























20 


























15 


s 


2 






















10 


/ 




/ 


3 
















5 


d 


a 




/ 


3. 


/ 










/ 































Totil 


IS 


£ 




£ 


S 


/ 










/ 








I 





















ii 



iKuabereiLutQaerfeaJ 



Udexoi 



Fig. 16. Showing the Scores op a 2* A Class on the Courtis Silent 
Reading Test No. 2. (Type IV.) 



over the several punctuation marks, not much growth in the 
power to comprehend the meaning in the printed page can 
be expected. Where the children study their reading lesson 
with the point of view of being able to respond in this way, 
they fasten upon themselves the habit of watching for words , 
whose pronunciation they are not sure of, or they form the 
habit of reproducing the sounds of syllables, thus estab- 



84 MEASURING THE RESULTS OF TEACHING 

lishing the practice of moving the lips and other speech 
organs when reading silently. Frequently both these habits 
fix themselves upon children whose reading is judged mainly 
by the daily oral performance. When either or both habits 
become fixed, a real struggle is required to break them. Un- 
less they are broken, however, the child suffers a severe 
handicap the rest of his reading life. Many men and women 
of mature years are still paying the price of those habits 
fixed in youth. They are able to read but little faster si- 
lently than they can pronounce the words orally, because 
their speech organs make all the motions of the successive 
words as the reading proceeds. 

An illustration of the result of over-emphasis upon oral 
reading. Judd ! gives the case of a girl in high school which 
illustrates the result of over-emphasis upon oral reading. 
The girl was getting on well in her school work, but "found 
it exceedingly difficult to keep up with her classes in home 
assignments." Reports from her various instructors brought 
out the following statements: 

She is a very satisfactory student in French because she thinks 
clearly, studies thoroughly, and pronounces easily and correctly. 
The only drawback to her work is a lack of confidence in herself, 
which leads her to lose her head occasionally and feel that she 
knows much less than is the case. In English she is an appreciative 
and careful student, a little slow at times in getting a grasp of 
things. She has certainly no serious weakness up to this point and 
frequently offers hints of superior work. In mathematics she is in 
the better section and stands eighth among eighty-five students. 
In general science her work has been very satisfactory and her 
grades are high. 

This girl is like many another student who is getting on all right 
so far as the school is concerned, but is doing it at great expenditure 
of effort. 

She was tested with a series of passages both in oral and silent 

1 Judd, C. H., Reading: Its Nature and Development. Supplementary 
Educational Monographs (University of Chicago Press), p. 161. 



CORRECTING DEFECTS IN READING 



85 



reading. . . . The figures show that in general the rates of silent 
and oral reading are very much alike. . . . 

There were marked tendencies to whisper all material read. She 
was much surprised when told not to do this and was sure she would 
not understand what she read because, as she said, she understood 
what she read only when she "heard" the words. 



Table 1 
Rate of Reading 



Tsr 



— T2T 

100" 



EX OF 

CHILDREN 
MJULlNC 
EACH 

SCORE- 



31 



1J£ 



Index of Comprehension. 



Diatno«I« 


CuMtwork 


baprtl 


(Mo.po.r^Jitio. 


alhUKMU 


tm*k*mm»mt 


QhGh 

Answered 


M 


Lm 

than 
-5 


-5 to 

+5 


6-3S 


10-69 


70-79 


80-84 


35-89 


90-94 


95-99 


100 




70 


























65 


























60 


























55 


























50 


























45 


























40 


(o 














/ 


/ 


3 


/ 




35 


H 












/ 






1 


a 




30 


3. 












/ 


1 










25 


V 










/ 


/ 




/ 




i 




20 


If 












3l 


* 


/ 


3 


i 




15 


H 










/ 




/ 


X 








10 


























5 

















































~7 




Total 


3/ 










5l 


S 


7 


s 


JL. 





























Medun Namber oi Lait QoestMD 



AanwteJ gLfl Median Index of Compreaeatioii //. 



il 



Fig. 17. Showing the Scores of a Sixth-Grade Class on the 
Courtis Silent Reading Test No. 2. (Type V.) 



The Remedy. The remedy for this type of situation, 
particularly below the sixth grade, is to place more emphasis 
upon silent reading. In doing this the suggestions given on 
page 59 will be helpful. 

Type V. Slow readers with a satisfactory index of com- 
prehension. Fig. 17 shows the record of a sixth-grade class 
which is deficient in rate of work. The median number of 



86 MEASURING THE RESULTS OF TEACHING 

words per minute is fifteen less than the standard and the 
median number of the last question is also fifteen below the 
standard. The index of comprehension is only four points 
below standard. These facts show that the pupils of this 
class read slowly and particularly answer questions slowly. 
However, they are careful readers as is shown by the index 
of comprehension. They need training in more rapid read- 
ing. The suggestions given on pages 66 and 68, apply to this 
type also. 

VI. Correcting Defects in Oral Reading 

The record of the scores of a class in the case of Gray's 
Oral Reading Test is not so helpful to a teacher as the 
records of the reading of individual pupils. This shows the 
types of errors which they made and a knowledge of them 
frequently will suggest the appropriate remedy. 

An illustration of individual instruction in oral reading. 
The fourth-grade teacher from whose report we quoted on 
pages 79 to 81 also dealt with oral reading. The "group" 
instruction described on page 80 applied in part to oral read- 
ing. This was supplemented by seven types of individual 
instruction. 

Type lesson 1. All look at the first phrase, looking up when they 
reach a comma or a period. When the entire group is looking at the 
teacher she nods and they repeat the phrase. She watches individ- 
uals to find their difficulties, but does not interrupt. When they 
have said all but the last word of the phrase they again look down, 
silently getting the next phrase and looking up, holding the phrase 
in mind until all are ready. Again the teacher nods and the group 
gives the phrase orally, looking down at the last word and con- 
tinuing this procedure to the end of the paragraph or section. 

The intensive study calculated to improve poor readers can be 
made to yield a double return, if, instead of selecting hard words 
and subjecting them to analytic study, the unit is the phrase or 
group of words which expresses an idea. Instead of working at a 
difficult word, the phrase in which it appears is studied until mas- 



CORRECTING DEFECTS IN READING 



87 



tered. Instead of working with one child at a time and giving each 
child only a few minutes of actual oral reading, four or five of those 
who have similar ability are grouped together, while other groups 
of poor readers follow silently. Third-grade material or very simple 
fourth-grade material is used for this purpose. 

While other pupils are being tested, the ones who have had Type 
1 answer mentally or in writing blackboard questions concerning 
the material of their lesson. Occasionally duplicated sheets con- 
taining uncompleted sentences or a story are used instead, the 
children filling in the blanks mentally or in writing. 

Type lesson 2. Eye training and focus. Field of vision enlarged 
to include several words rather than one. First, by having the 
book far enough from the eyes. Secondly, by eliminating the use 
of a finger or other place-keeping device. Thirdly, by work with 
flash cards, flashing phrases, trying to get a phrase at one flash, and 
counting the number of flashes needed for each phrase. These 
phrases were cut from current printed matter and mounted on 
small cards. Written sentences directing children to perform cer- 
tain activities were also used as flash material. The one who first 
read the direction carried it out. The one who had three such op- 
portunities in succession was given a sheet with similar work for 
silent reading and could return to the group when finished. 

Type lesson 5. Differentiation for pupils who confuse similar 
words or miscall syllables, guess at words, or omit endings. Lists 
like the following form the basis of such work. Lists are compiled 
from actual mistakes made by children : 



that 


woman 


beautifully 


swimming 


when 


every 


prettiest 


board 


what 


never 


prettily 


close 


then 


even 


probably 


chose 


how 


ever 


lovingly 


lying 


who 


very. 


companions 


buying 


their 


these 


understand 


tired 


there 


those 


understood 


tried 


than 


now 


laughingly 


certain " 


women 


know 


quietly 


curtain 


man 


beautiful 


left 


felt 



Type lesson 6. Lessons in accuracy for those who make errors, 
substitutions, and omissions; reading a page orally and counting 
errors, or reading until they make an error to see how many lines 
they can read perfectly. 




88 MEASURING THE RESULTS OF TEACHING 

Type lesson 7. Breathing exercises. Children taught to breathe 
rhythmically at ends of phrases or clauses instead of breaking the 
smoothness of oral reading. Practice in breath control is thus re- 
lated to the problem of meaning and interpretation. Abdominal 
breathing taught. 

Type lesson 8. Articulation exercises for mumblers, or those with 
other bad speech habits. 

Type lesson 9. Voice work and expression. Unpleasant voice 
quality and monotony corrected by special practice and training. 
Children are taught to vary meaning by change of stress and to 
show relative importance of ideas similarly. Punctuation is studied 
for the same purpose. 

The Results. For oral reading very striking results were 
obtained. They are shown graphically in Fig. 18. The in- 
crease in the closeness of the grouping of the members of the 
class is significant as well as the progress made by the indi- 
vidual pupils. 

The base line represents lines read per minute. The lettered 
blocks represent individuals. The group divisions are shown by 
vertical lines. Thus pupil O was in Group "D" and read five lines 
per minute in November, moved to Group "C" in December, and 
was reading nine lines per minute. In January he read twelve lines 
per minute and was in Group "B." In February he read thirteen 
lines per minute, but did not get into Group "A" until March. 
. . . The reading rate is an average of from three to five trials on 
as many selections of unstudied material from the Horace Mann 
Reader. No rate of measurement was made in April, as other 
reading tests were conducted. 1 

Interpretation of scores in ungraded schools. In rural 
schools or other ungraded schools classes are frequently so 
small that it is not wise to use the median or class scores. 
The interpretation is largely a matter of comparing the 
scores of individual pupils with the standards. In doing this 
certain facts should be kept in mind. First, the standards 
are median scores. For example, the standards for the fifth 

1 Elementary School Journal, vol. 18, p. 512. 



CORRECTING DEFECTS IN READING 89 



r o 



R S P 



S 



November 



d c 



I I l„ I 



20 



N 



I I I! 



S T Q R 



I 



December 



January 



ST R 



»5 '20 

A February 

H 



J5 



20 



l i i i i i „ i i 



I 



March 



T R B P 



May 



B C 



5 10 IS 20 

BOB A 

Fig. 18. Showing Improvement in Oral-Reading Rate of Twenty- 
fourth when Individual and Group Instruction was used. Rate 
expressed in Lines per Minute. (After Zirbes.) 



90 MEASURING THE RESULTS OF TEACHING 

grade are the median scores of several thousand fifth-grade 
pupils. Thus half of these pupils had scores greater than the 
standard scores and half of them had scores less than the 
standards. Second, pupils of the same grade differ widely 
in ability, and when the class scores are up to standard, half 
of the class will be above standard and half will be below. 
Third, in schools where only a few pupils belong to a grade, 
it may be that all are pupils of little natural ability, and 
hence should not be expected to have scores up to standard. 
On the other hand, it may be that they have a high degree 
of natural ability and should have scores distinctly above 
standard. 

This makes the interpretation of the scores of individual 
pupils or of small groups of pupils difficult and somewhat 
uncertain. However, it is safe to say that when a pupil is 
distinctly below standard in rate or comprehension of silent 
reading, or both, his case should be carefully studied by the 
teacher. Much of what has been said concerning the causes 
of class weaknesses and the correctives for them also applies 
to individual pupils. Some pupils will be found to be high 
in rate, but low in comprehension (the rapid, careless reader; 
see pages 51 to 58 ) ; others will be low in rate, but relatively 
high in comprehension (the slow, plodding, but careful 
reader; see pages 65 to 68); still others will be low in both 
rate and comprehension (the slow, careless reader or one 
who has not learned to read; see pages 73 to 79). . 

Some pupils will be found who are distinctly above stand- 
ard in both rate and comprehension. In such cases the 
teacher's problem is different. These have made satisfactory 
progress in silent reading under the instruction which they 
have been receiving and thus they require no special atten- 
tion. The only case in which a modification of the instruc- 
tion should be made is when a pupil who is above standard 
in silent reading is not doing satisfactory work in arithmetic, 



CORRECTING DEFECTS IN READING 91 

spelling, or some other subject. Then he should spend less 
time reading and more upon the subject in which he is weak. 

The rural teacher's opportunity for diagnosis and correc- 
tive instruction. When a teacher has a small number of 
pupils, he has an unusual opportunity for diagnosing his 
pupils and applying the required corrective instruction. 
Each pupil can be studied until his strong points and his 
weaknesses are known. Upon the basis of this information 
the teacher can easily apply the correctives because the in- 
struction is largely individual anyway. The teacher who has 
twenty-five or more pupils in one class has much less oppor- 
tunity to deal with individual pupils. When the teacher 
knows the scores of the pupils of his class on standardized 
tests, each pupil can be given that kind of instruction 
which he needs and under which he will make the greatest 
progress of which he is capable. 

The use of standardized tests does not require a large 
amount of time. To teachers who may be interested in such 
diagnostic and remedial work this comment by the author 
of the above report is significant. (See pp. 79 and 86.) 

This study was not conducted by a specialist, but by a grade 
teacher interested in the advancement of the class through methods 
which reach the individual members. No time was taken from 
other studies. In fact a similar experiment in individual instruction 
was simultaneously carried on in spelling, arithmetic, and penman- 
ship. The results were tested and are evidence that no one subject 
was over-stressed. The time economy, resulting from scientific 
procedure, also made possible a fullness and breadth of teaching 
usually thought incompatible with standardization and educa- 
tional measurement. 1 

Summary. The ideas presented in this chapter may be 
summarized under three heads: 

(l) Service of standardized tests to the teacher. By far the 

1 Elementary School Journal (March, 1918), p. 522. 



92 MEASURING THE RESULTS OF TEACHING 

largest service of standardized tests in reading is being 
rendered to the teacher. Not only are they enabling the 
teacher to check up his conception of what can justly be 
expected of children, but they are indelibly impressing 
upon his mind the absolute need for recognizing the indi- 
vidual differences among his pupils in respect to each 
problem of learning, and for studying the reading needs of 
his pupils in order to plan the instruction most wisely. In 
this chapter we have considered the meaning of certain 
types of class records, how to secure additional information 
concerning the reading abilities of pupils and the general 
correctives which should be applied to improve the stand- 
ing of such classes. For certain cases we have given illus- 
trations of the detailed diagnosis of pupils, the correctives 
which were applied, and the results which were obtained. 

The distinction between silent reading and oral reading 
has been emphasized. The teacher should bear in mind that 
a pupil may read well orally from his reader, but may be 
doing poorly in geography or in the problems of arithmetic 
because he has not learned to read silently. These content 
subjects depend upon reading, but not upon the sort of 
oral word-pronouncing which still too largely characterizes 
our reading periods. Such a child needs a different sort 
of reading. He would be found to stand low, probably, in 
vocabulary; probably low in quality of silent reading. If 
the teacher has before him a chart upon which is recorded 
the standing of this child in the various aspects of reading, 
he will no longer assign for his study the next page or two 
in the Reader. He needs the sort of reading which widens 
his vocabulary more rapidly and centers his thought upon 
meaning instead of upon words. 

As an illustration l of the aid of reading tests in such 

1 Uhl, W. L., "The Use of the Results of Reading Tests as a Basis for 
Planning Remedial Work"; in Elementary School Journal (December, 
1916), vol. 17, no. 4. 



CORRECTING DEFECTS IN READING 93 

diagnosis, the case of the Training School at Oshkosh, Wis- 
consin, may be cited. During a summer term of only six 
weeks, pupils, by use of the Kansas Silent Reading Tests, 
the Gray Oral Test, and the Gray Silent Reading Tests, had 
their difficulties localized. Instruction was then given upon 
the points revealed to be needing attention. Twenty out of 
one hundred and five children were given different instruc- 
tion from that given the class as a whole. Surprisingly 
greater results were obtained in the case of those children 
whose instruction was specifically adapted to their diffi- 
culties. 

(2) Service of standardized tests to the rural teacher. Stand- 
ardized tests render a peculiar service to rural teachers by 
setting standards for them. A teacher who works in isola- 
tion from other teachers needs to know how her pupils com- 
pare with pupils in other schools. Since standardized tests 
have been widely used, they furnish a means by which any 
teacher can easily ascertain how her pupils stand in com- 
parison with the established standards. 

(3) Service of standardized tests to the child. Since the begin- 
ning of schools children have been sent to school to be 
taught. That being the case, they wait to be told what to 
do, and there is the end of their responsibility. When the 
end of the month comes they look to their report card for 
a measure of their success in doing what they have been 
told. 

A function of standardized tests, by which the child can 
measure his own achievements about as successfully as the 
teacher can, is that they bring the child into partnership 
with the teacher in directing the whole educative process. 
If the child discovers by actual trial that he has only three 
fourths as large a vocabulary as children of his grade the 
country over, or that he reads only three fourths as fast, 
he can be depended upon better to cooperate in overcom- 



94 MEASURING THE RESULTS OF TEACHING 

ing the fault than when he is simply given a card every 
month with 70 assigned to his reading. Particularly is this 
true if he feels that at the end of a given period he can take 
his own measure again to ascertain his gain. Children 
should be enlisted with the teacher in the effort to select 
the most needful sorts of materials for their study. Where 
one child needs problem-solving, another needs a story, 
while still another needs something else than reading of 
any kind. 

Service of standardized tests to the superintendent. Al- 
though this book is written primarily for teachers, it will not 
be out of place to call attention to the usefulness of stand- 
ardized tests to the superintendent or supervisor. From the 
importance of reading in the general efficiency of all school 
work we may assume that the superintendent is vitally 
interested in making the instruction in reading most effec- 
tive. What can reading tests reveal to him? 

First, they can satisfy him and his teachers of the general 
status of reading in his district. It is easy for any superin- 
tendent to carry conviction among his teachers that the 
results in reading are not satisfactory in his district if he can 
show that among a group of a dozen or more neighboring 
cities his district stands low. The extent to which it stands 
low becomes a measure of the renewed earnestness needed in 
attacking the problem of improvement. 

It is difficult for one to carry in mind a fixed standard of 
achievement. One gradually thinks more and more in terms 
of what those around him are achieving. It would have been 
quite impossible, for example, to convince the superintend- 
ent and teachers of the Anglo-Korean school at Songdo, 1 
without a standardized test, that the children in their fifth 

1 Wasson, Alfred W., "Report of an Experiment in the Use of the Kansas 
Silent Reading Tests with Korean students"; in Educational Administra- 
tion and Supervision, vol. 3, p. 98. 



CORRECTING DEFECTS IN READING 95 

grade could do, on the average, reading work valued at only 
3.8 units, while American children, who had been in school 
only the same number of years, could score 13.2 units, or 
that their sixth grade could accomplish only as much as the 
American third grade. It meant much to that school for its 
superintendent and teachers to be able to measure their 
school by the American standards. 

Reveal wrong emphasis in teaching. Differences in the 
reading work done in the several buildings within a city may 
be as striking as differences among cities. In a certain Mid- 
dle-Western town a forceful principal of one of the ward 
buildings has dominated the work of the building for a good 
many years. The reading of the building was his particular 
pride. When tested for silent reading ability his children 
scored in every grade but little more than half what the 
children in another building scored where the work was re- 
puted to be "much less thorough." These results were made 
the basis of deliberations among the teachers as to the legiti- 
mate outcomes of reading, with the result that, without 
diminishing any one's zeal, the emphasis was transferred 
from oral word-pronouncing to silent thought-getting in the 
building where this strong principal dominates the work so 
effectually. 

QUESTIONS AND TOPICS FOR STUDY 

1. What are the chief methods by which adults add new words to their 
vocabularies? Are more new words learned from the context in which 
they appear, or from the dictionary? What can you say concerning 
the best way to increase the vocabulary of children? 

2. What are some of the other factors besides vocabulary involved in 
silent reading? In what grades is vocabulary the most important fac- 
tor? Make some suggestions for guaranteeing the intimate association 
of the mental concept which a word symbolizes, and the word itself 
when it is encountered in word drills. 

3. What is the significance of rate in reading? Is there any truth in the 
rather common belief that one who reads slowly "gets more out of 
what he reads"? If you do not know the answer, can you devise some 



96 MEASURING THE RESULTS OF TEACHING 

way to test it out in your class? Compare your own silent reading 
rate with that of some equally well-educated friends. 

4. What are the chief dangers involved in having much oral reading in 
the lower grades? Can these dangers be safeguarded? What types of 
reading matter do you now read orally outside the schoolroom? Are 
these the types which your pupils are asked to read orally? 

5. What are the circumstances under which you last read aloud? Do 
your pupils have the same incentives for reading clearly and inter- 
estingly that you had on that occasion? 

6. What are some of the things you do to assist your pupils in developing 
ability to comprehend the meaning of the printed page? Do you know 
of faulty habits which some of them have which prevent their center- 
ing attention upon the meaning? Do you know which pupils read 
with accuracy? Which with rapidity? 

7. How long does it take you to become familiar with the reading diffi- 
culties of each child when you receive a new class of, say, thirty chil- 
dren? Would you consider it economical if some tests were available 
by means of which you could discover these difficulties as well as 
others the first day and thus prepare a chart of each child's instruc- 
tional needs? How long at the beginning of a term could you afford 
to spend in making such a diagnosis? 

8. Think of the last examination you gave in reading. Did it test satis- 
factorily what you are striving to teach in reading? 



CHAPTER IV 

THE MEASUREMENT OF ABILITY IN THE OPERATIONS 
OF ARITHMETIC 

How arithmetical ability is measured. The plan of meas- 
uring the ability of pupils to do the operations of arithmetic 
is to have them do a set of examples l under specified condi- 
tions. In order that the scores may have a definite meaning, 
the test is limited to one type of example in one operation, 
as subtraction or multiplication or at most to a group of 
closely related types. The necessity for determining the 
value of the different examples in the test can be elim- 
inated by constructing the examples so that they con- 
tain the same number of combinations; that is, in addition 
having each example involve twenty additions. The rate at 
which the pupil performs the operations is measured by 
timing the test as was done in the measurement of the ability 
to read silently. In the following pages we will describe two 
tests which have been devised to measure the ability of 
pupils to do the operations of arithmetic. 

I. Courtis Standard Research Tests, Series B 

Description of tests. The Standard Research Tests, Series 
B, or, as they are commonly called, the Courtis Arithmetic 
Tests, have been more widely used than any other instru- 
ment for measuring arithmetical abilities, and as a result 
we have better comparative standards for their use. The 

1 The word "problem" is used by some writers to designate both "ex- 
ample" and "problem." In this book the word "example" will be used 
to designate exercises which explicitly call for certain arithmetical oper- 
ations. The word "problem" will designate only those exercises which 
require the pupil to determine first what operations are to be performed. 



98 MEASURING THE RESULTS OF TEACHING 

series consists of four tests, printed on four consecutive 
pages. They are suitable for a general survey of the abilities 
of pupils to perform the operations with integers. They are 
used in Grades four to eight. 

Test No. 1. Addition 

The twenty-four examples of this test have been con- 
structed so that all have the same form, three columns 
of nine figures each. The following are samples. Time 
allowed, 8 minutes. 

927 297 136 486 384 176 



379 


925 


340 


765 


477 


783 


756 


473 


988 


524 


881 


697 


837 


983 


386 


140 


266 


200 


924 


315 


353 


812 


679 


366 


110 


661 


904 


466 


241 


851 


854 


794 


547 


355 


796 


535 


965 


177 


192 


834 


850 


323 


344 


124 


439 


567 


733 


229 



In giving the test the pupils are directed as follows: 

You will be given eight minutes to find the answers to as many 
of these addition examples as possible. Write the answers on this 
paper directly underneath the examples. You are not expected to 
be able to do them all. You will be marked for both speed and ac- 
curacy, but it is more important to have your answers right than 
to try a great many examples. 



Test No. 2. Subtraction 

This test consists of twenty -four examples, each involving 
the same number of subtractions. The following are sam- 
ples. Time allowed, 4 minutes. 

107795491 75088824 91500053 87939983 
77197029 57406394 19901563 72207316 



THE OPERATIONS OF ARITHMETIC 99 

Test No. 3. Multiplication 

This test consists of twenty-four examples of this type. 
Time allowed, 6 minutes. 



»46 


3597 


5739 


2648 


9537 


29 


73 


85 


46 


92 



Test No. J^. Division 

This test consists of twenty-four examples of this type. 
Time allowed, 8 minutes. 

25 )6775 94 )85352 37 )9990 86 )80066 

73 )58765 49 )31409 6 8)43520 5 2)44252 

Each of the examples of a test calls for the same number of 
operations under approximately the same conditions. This 
makes the examples of each test approximately equal in 
difficulty. Any example of the addition test, say the seventh, 
is just as difficult as any other, say the second. Thus, the 
tests consist of twenty-four equal units, just as a yardstick 
consists of thirty-six equal units (inches). The measure of 
a pupil's ability is represented by the distance he advances 
along the scale in the given time; that is, by the number of 
examples done and by the per cent of these examples which 
have been done correctly. 

Since an example of one of these tests is defined as so many 
operations under certain conditions, it is possible to con- 
struct other tests equal in difficulty. Four forms have been 
constructed. This makes it possible to use a different form 
when the tests are given a second time. 

Giving the tests. The general directions for giving read- 
ing tests also apply in the case of arithmetic. (See page 25.) 
Detailed directions accompany these tests. Since the same 
tests are given in all grades, a group of pupils belonging to 



100 MEASURING THE RESULTS OF TEACHING 

two or more grades can be tested together. It is only neces- 
sary to sort the papers according to classes when recording 
scores. If it is not convenient or desirable to give the four 
tests on one day, the test papers may be collected and re- 
turned the next. 

Marking the papers. In marking the test papers, which is 
done by the use of a printed answer card that is run along 
across the page, no credit is given for examples partly right 
or for examples partly completed. This simple plan of mark- 
ing the papers insures uniformity and accuracy. A pupil's 
score is the number of examples attempted and the number 
right. The number of examples attempted is a measure of 
the pupil's rate of work. By dividing the number right by the 
number attempted, the per cent of examples correct may be 
obtained. This is a measure of the quality or accuracy of his 
work. Thus, the two "dimensions" of the ability to do the 
operations of arithmetic are rate and accuracy. 

Recording the scores of a class. For recording the scores 
of a class a record sheet of the form shown in Fig. 19 is used. 
This figure contains merely the blank for addition, but the 
forms for the other three tests of the series are identical with 
it. Detailed instructions for recording scores are printed on 
the record sheet. The large figures at the top of the sheet 
refer to the number of examples attempted and the small 
figures within the squares refer to the number of examples 
done correctly. The sheet is arranged so that the per cent 
of examples done correctly is computed automatically and 
the distribution of the scores according to both rate and 
accuracy is obtained at the same time. The scores of a 
seventh-grade class are shown in Fig. 19. The numbers 
written in certain of the squares represent the number of 
pupils whose scores fell within these divisions of the record 
sheet. The distribution according to rate is found at the 
bottom of the record sheet and is to be read thus: Three 



»<^ 


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1 








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1 


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ei 


3 


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3 


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102 MEASURING THE RESULTS OF TEACHING 

pupils attempted only six examples, two pupils attempted 
only seven examples, five pupils attempted only eight ex- 
amples, etc. The distribution according to accuracy is found 
at the right-hand side of the sheet and is to be read thus: 
The per cent of examples done correctly by two pupils was 
less than fifty per cent, for five pupils it was between fifty 
per cent and sixty per cent, for five other pupils it was be- 
tween sixty per cent and seventy per cent, etc. These two 
distributions, the one according to the per cent of examples 
done correctly and the other according to the number of the 
examples attempted, describe the ability of the pupils of 
this class to do the examples of the addition test. 

Calculating the median score of a class. The central tend- 
ency (median) of the distribution of scores in the case of 
silent reading was found by arranging the test papers in 
order and counting up to the middle paper. The score on 
this paper was the median score. (See page 28.) This is not 
the best method to use here. For calculating the median, 
Courtis gives explicit directions in Folder D which is de- 
signed to accompany this series of tests. We give here gen- 
eral directions for finding the median so that they can be 
conveniently referred to. 

The median is the mid-measure of a distribution. In the 
case of a distribution having an odd number of scores it is 
the value of the middle score. If there is an even number of 
scores it is halfway between the two middle scores. 

Table XII gives a group of scores in the form of a distribu- 
tion. The column labeled "Score*' gives the scores arranged 
in order of magnitude. The column headed "Frequency" 
tells how many scores there are of each magnitude, or how 
frequently each score occurs. In this table there are two 
scores of 13, two scores of 12, five scores of 11, etc. The total 
number of scores is 45. The twenty-third score is the mid- 
dle one, but it is not possible to identify its value di- 



THE OPERATIONS OF ARITHMETIC 103 

Table XII. Showing a Typical Distribution of Scores 
in Number of Examples attempted * 

Score Frequency * 

n 1 

13 2 

12 2 

11 5 

10 9 

9 7 

8 8 

7 5 

6 3 

5 2 

4 1 

3 

2 

Total.. 45 

Approximate median 9.0 

Correction 6 

True median 9.6 

* The frequency is the number of pupils making the score indicated. The scale consists 
of the scores arranged in order. 

rectly. It is clearly one of the seven scores given as 9, 
because counting from the lower end of the distribution, 
1 and 2 are 3, and 3 are 6, and 5 are 11, and 8 are 19, and 
7 are 26, which is beyond the middle of the distribution. 
Therefore the approximate value of the median of this dis- 
tribution is 9.0, which is the interval which contains the 
true median. 

Rule for finding median. (1) Find the half sum of the 
distribution. In case there is an even number of scores, 
there is no middle score. In such a case the average of the 
two most central scores may be taken, although for practical 
purposes it will be satisfactory to take the lesser of the two 
middle scores. By doing this the calculation of the median is 
made simpler. Thus, if a distribution contains forty-one 
scores, the middle score is the twenty-first score; if it con- 
tains forty scores, the twentieth score may be taken as the 



104 MEASURING THE RESULTS OF TEACHING 

middle score. 1 The number of the middle score is obtained 
by dividing the total number of scores by two. This quo- 
tient, expressed as the nearest integer, is called the "half 
sum." When using a particular test the directions which 
accompany that test should be followed, because the medi- 
ans used for standards have been obtained by following the 
accompanying directions. 

(2) To determine the approximate median it is simply 
necessary to locate the interval of the distribution in which 
the median falls. To locate the interval in which the median 
falls, begin at the lower end of the distribution and add to- 
gether the frequencies until the addition of the next one will 
make a sum greater than the number of the median score, 
or half of the total of the frequencies. This sum of the fre- 
quencies is called the "partial sum." The median score is 
in the next interval, and the approximate median is the 
value of that interval. 

(3) To calculate the amount to be added to the approxi- 
mate median to make the true median, proceed as follows: 
(1) Subtract the partial sum of the frequencies from the half 
sum. The partial sum is found in determining the approxi- 
mate median. (2) Divide this difference by the number of 
scores which are included in the interval in which the true 
median falls. Add this quotient to the approximate median. 

1 There is a difference of practice on this point. The directions which 
accompany the Monroe Standardized Silent Reading Tests read as follows: 
"The median score is the score on the middle paper in the pile of papers 
arranged according to size of scores. If there are thirty-five papers, the 
median score is the score on the eighteenth paper. If there are thirty-six 
papers, the median score is halfway between the score on the eighteenth 
paper and the score on the nineteenth paper." 

The directions which accompany the Courtis Standard Research Tests 
in Arithmetic, Series B, read as follows: "If there are thirty-seven chil- 
dren in the class, the nineteenth score in order of magnitude would be the 
median score; for there would be eighteen scores larger and eighteen smaller. 
If there were thirty-six children in the class, the eighteenth score would be 
taken as representing the nearest approximation to the middle measure." 



THE OPERATIONS OF ARITHMETIC 105 

If the width of the interval is more than one unit, the quo- 
tient must be multiplied by the number of units the interval 
contains. It is well to carry the quotient to two decimal 
places, but in writing the median it should be expressed only 
to the nearest tenth. 1 

The rule applied. In Table XII the half sum is 23. The 
approximate median is 9.0. The partial sum being 19, four 
of the seven scores in the 9-interval are required in order 
to reach the mid-point of the distribution. Four divided by 
7 is .6, which, added to 9.0, gives 9.6 the true median. 

Special cases. Although the rule given applies to all cases, 
there are a few special cases which sometimes give trouble. 
In Table XIII we show three special cases which may arise 
in using Series B. Case A is where the partial sum (13) is 
also the half sum (13). The approximate median is in the 
next interval (9). Since the difference between the partial 
sum and the half sum is zero, there is no correction and the 
true median is also 9.0. Case B is where the median falls 
in the first interval (0 to 49). It is only necessary to re- 
member that the width of this interval is 50. Case C is 
where the median falls in the 100-interval. The width is 
zero. Hence the correction is zero. 

Efficiency. Courtis has defined a measure of "efficiency." 
He says: 

The word "efficiency" as applied to education has, only too 
frequently, but little meaning. As used in connection with the 
Courtis Tests, however, it has a very definite meaning as soon as 
the following definition has been accepted: The efficiency of any 
teaching process which has a measurable product is the per cent of 
the total product that measures up to the standard for the grade. 

For each test find the sum of all the frequencies equal to or exceed- 
ing the standard. Multiply this sum by 100 and divide by the total 
number of scores. The result will be the efficiency for that test. 

1 See King, W. I., The Elements of Statistical Method, pp. 129-30; and 
Thorndike, E. L., Mental and Social Measurements, p. 54. 



106 MEASURING THE RESULTS OF TEACHING 

In Fig. 19 lines have been drawn to mark off those scores 
which are up to standard in both rate (11) and accuracy 
(100). There are three such scores. The efficiency of this 
class thus is 300-^39, or 7.7. However, many users of 
Series B do not believe the efficiency score has an important 
significance and it is not generally used. 

Table XTTT. Showing Three Special Cases in calculating 
the Median which arise in Using Courtis's Standard Re- 
i search Tests, Series B 

a b c 



Scale 


Frequency Scale 


Frequency Scale Frequt 


15 




100 


1 


100 15 


14 


.. 


90- 99 




90-99 1 


13 


1 


80- 89 


2 


80- 89 4 


12 


1 


70-79 


2 


70- 79 3 


11 


2 


60- 69 


1 


60- 69 2 


10 


3 


50- 59 


4 


50- 59 


9 


5 


0- 49 


14 


0- 49 


8 


4 




— 


— 


7 


6 


Total.. 


24 


Total 25 


6 
5 


3 








Approximate median 0.0 


Approximate median 100 


4 


.. 


Correction.. .... 


... 43.0 


Correction 



Total. 



25 True median 43.0 True 



100 



Approximate median 9 . 
Correction 

True median 9.0 



Standard median scores. In Table XIV there are given 
three standard scores. (1) General median scores based 
upon distributions of "many thousands of individual scores 
in tests given in May or June, 1915-16. The distribution 
for each grade was made up of approximately equal numbers 
of classes from large-city schools and from small-city and 
country schools." (2) The standards proposed by Courtis 
after three years' use of these tests. (3) Boston standard 
median scores after the tests had been used for three years. 



THE OPERATIONS OF ARITHMETIC 107 

These standards are given in terms of rate and accuracy, 
which is the best form. However, for certain purposes it 
may be desirable to have them in terms of "number at- 
tempted" and "number right." The number of examples 
right can be found by multiplying the number of "examples 
attempted" or the rate by the accuracy. 

With reference to the standards which he has proposed 
Courtis says: 

The speeds [rates] set as standard are approximately the average 
speeds [rates] at which the children of the different grades have 
been found to work when tested at the end of the year, when for 
any one grade a random selection of five thousand scores from 
children in schools of all types and kinds are used as a basis of 
judgment. 

Standard accuracy is perfect work, one hundred per cent. This 
is a tentative standard only, as there is available very little infor- 
mation in regard to the factors that determine accuracy and the 
effects of more efficient training. 

At present in addition and multiplication it is only very excep- 
tional work in which the median rises above eighty per cent accu- 
racy, while in subtraction and division the limiting level is ninety 
per cent. 

Standard speeds [rates] are not likely to change greatly. Stand- 
ard accuracy is surely destined to approach much more nearly one 
hundred per cent than present work would indicate. 

Standard scores are not only goals to be reached; they are limits 
not to be exceeded. It seems as foolish to overtrain a child as it is 
to undertrain him. All direct drill work should, in the judgment of 
the writer, be discontinued once the individual has reached stand- 
ard levels. If his abilities develop further through incidental train- 
ing, well and good, but the superintendent who, by repeated raising 
of standards, forces teachers and pupils to spend each year a larger 
percentage of time and effort upon the mere mechanical skills, 
makes as serious a mistake as the superintendent who is too lax in 
his standards. 1 

1 Courtis, S. A., Third, Fourth, and Fifth Annual Accountings, 1913-16 
(Department of Cooperative Research, Detroit), p. 49. 



108 MEASURING THE RESULTS OF TEACHING 



Table XIV. Standard Median Scores, Courtis's Standard 
Research Tests, Series B 





Addition 


Subtraction 


Multiplication 


Division 


Grade 


i 


I 


4 


I 


1 


1 


1 


3 


IV. General 

Courtis 

Boston 

V. General 

Courtis 

Boston 

VI. General 

Courtis 

Boston 

VII. General 

Courtis 

Boetoif 

VIII. General 

Courtis 

Boston 


7.4 

6 

8 

8.6 

8 

9 

9.8 
10 
10 

10.9 

11 

11 

11.6 

12 

12 


64 
100 
70 

70 
100 
70 

73 

100 
70 

75 
100 
80 

76 
100 
80 


7.4 

7 

7 

9.0 

9 

9 

10.3 

11 

10 

11.6 

12 

11 

12.9 
13 

12 


80 
100 
80 

83 
100 
80 

85 
100 
90 

86 
100 
90 

87 
100 
90 


6.2 

6 

6 

7.5 

8 

7 

9.1 

9 

9 

10.2 

10 

10 

11.5 

11 

11 


67 

100 

60 

75 

100 
70 

78 
100 
80 

80 
100 
80 

81 
100 
80 


4.6 
4 

4 

6.1 

6 

6 

8.2 

8 

8 

9.6 
10 
10 

10.7 

11 

11 


57 
100 
60 

77 
100 
70 

87 
100 
80 

90 
100 
90 

91 

100 
90 



Comparisons of class scores with the standards given in 
Table XIV or any others are valid only when the tests have 
been given under standard conditions. Slight changes in the 
method of giving the tests may affect the scores as much as 
the difference in the standards from one grade to another. 

The interpretation of scores. The standards for Series B 
are to be used for the interpretation of individual and class 
scores in much the same way as the standards for the read- 
ing tests. The form of the class record sheet is convenient 
for interpreting the scores of the class. If one will draw a 
vertical line to represent the standard rate and a horizontal 
line to represent the standard accuracy for the grade, one 
can tell at a glance what the condition of the class is. See 
Fig. 21, page 120. 

Graphical representation of the scores of a school. In Fig. 



THE OPERATIONS OF ARITHMETIC 109 

20 there is shown a scheme devised by Courtis for the 
graphical representation of the median scores of ;i a city or 
school building. The position of the standards is shown by 
the circles along the dotted-line curve. The position of the 
median scores of a city is shown by the X's through which 
the solid-line curve passes. This is a very effective means 
for showing the condition within a city or school. The figure 
makes it very clear that the median scores for number of 
examples attempted are conspicuously below standard. The 
position of the first X which represents the fourth-grade 
scores is below and to the left of the fourth-grade circle. 
This means that the fourth-grade scores are below standard. 
The fifth grade shows an increase in accuracy but the pupils 
do not work more rapidly than those in the fourth grade. 
From the fifth grade to the sixth and from the sixth grade to 
the seventh growth is shown, principally in accuracy. For 
number of examples attempted the seventh grade is below 
the fifth-grade standards. The eighth grade shows an in- 
crease in rate of work but a marked decrease in accuracy. 

II. Monroe's Diagnostic Tests 

Arithmetical abilities distinct. A few years ago Stone 1 
investigated the nature of ability in arithmetic and con- 
cluded that it was made up of a number of specific abilities. 
His conclusions have been corroborated by a number of 
other investigations, 2 and it is now reasonably certain that 

1 Stone, C. W., Arithmetical Abilities and Some Factors Determining 
Them. (Teachers College Contributions to Education, no. 19, 1908.) 

2 Kallom, Arthur W., Determining the Achievement of Pupils in Addition 
of Fractions. (School Document, no. 3, 1916. Boston Public Schools.) 

Recently an investigation was made, under the direction of the writer, of 
the nature of the ability to place the decimal point in a quotient. This 
investigation showed that a number of specific abilities were involved, 
and not a single ability. See Monroe, Walter S., " The ability to place the 
decimal point in division," Elementary School Journal, vol. 18, pp. 287-93 
(December, 1917). 



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THE OPERATIONS OF ARITHMETIC 111 

in teaching the operations of arithmetic, we are attempting 
to engender a number of specific abilities which are relatively 
distinct, and not a single arithmetical ability. The word 
"ability" is used to refer to the rate and accuracy with 
which a pupil does a certain type of example. Teachers 
have recognized that pupils could do subtraction examples 
in which there was no " borrowing " when they were unable 
to do examples in which there was "borrowing," or that 
they could do short division when they were unable to do 
long division. The investigations of Stone and others have 
proven that there are as many different abilities as there 
are types of examples. In fact, it is obvious that the abil- 
ity to add a column of three figures is not the same as the 
ability to add a column of twelve figures. In adding a col- 
umn of figures it is necessary that one hold in mind the 
partial sum until he has added the next figure. This process 
must be repeated until the final sum is reached, and a fail- 
ure to do this continuously will result in stopping the add- 
ing, at least temporarily. It is a frequent occurrence, for 
one who is not accustomed to adding long columns of fig- 
ures, to find that he has stopped, perhaps has even lost 
the partial sum, and must begin again. The span of atten- 
tion required in adding three figures is short, and pupils 
who are able to do examples of this type with a high degree 
of skill frequently are unable to add long columns of figures 
with an equal degree of skill. In fact, we have no reason 
to expect them to be able to do this type of example until 
they have practiced upon it. 

Courtis, 1 the author of the Standard Research Tests, has 
identified the following types of examples in the operations 
with integers: 

Addition: (1) addition combinations; (2) single-column 

1 Courtis, S. A., Teacher's Manual for Courtis Standard Practice Tests 
(1916.) 



112 MEASURING THE RESULTS OF TEACHING 

addition of three figures each; (3) "bridging the tens," as 
38 + 7; (4) column addition, seven figures; (5) addition 
with carrying; (6) column addition with increased attention 
span, thirteen figures to the column; (7) addition of numbers 
of different lengths. 

Subtraction: (1) subtraction combinations; (2) subtrac- 
tion of 9 or less from a number of two digits, without " bor- 
rowing"; (3) same as the second, but with "borrowing"; 
(4) subtraction of numbers of two or more digits involving 
borrowing. 

Multiplication: (1) multiplication combinations; (2) mul- 
tiplicand two digits, multiplier one digit, and no carrying; 
(3) same as number 2, but with carrying; (4) long multipli- 
cation, without carrying; (5-8) zero difficulties, four types: 

560 807 617 703 

40 59 508 60 

(9) long multiplication, with carrying. 

Division: (1) division combinations; (2) simple division, no 
carrying; (3) same as number 2, but with carrying; (4) long 
division, no carrying; (5-6) zero difficulties, two cases: 

690 302 

71)48990 31)9362 

(7) long division, with carrying, "first case, the first figure 
of the divisor is the trial divisor and the trial quotient is the 
true quotient": 

72 
• 63)4536 

(8) "second case, where the trial divisor is one larger than 
the first figure of the divisor, but the trial quotient is the 
true quotient " : 

63 
49)3087 



THE OPERATIONS OF ARITHMETIC 113 

(9) "third case, where the first figure of the divisor is the 
trial divisor, but the true quotient is one smaller than the 
trial quotient": 

89 
63)5607 

(10) "fourth case, where the first figure of the divisor must 
be increased by one to obtain a trial divisor and the second 
trial quotient must be increased by one to get the true 
quotient)": 

79 
36)2844 

Each a specific habit. Each of these types of examples 
requires a specific habit or automatism. To be sure, certain 
elements, such as the fundamental combinations, are com- 
mon, but careful analysis will show that the ability to do 
examples of one type is different from that required to do 
another. Not only will a careful analysis reveal this fact, 
but it has been repeatedly demonstrated by carefully con- 
ducted investigations. In addition to the specific auto- 
matisms which are required for the four fundamental op- 
erations with integers, a number of other automatisms are 
required for the operations with fractions both common and 
decimal. At present we have only partial analysis of the 
examples in these fields, and for that reason it is not possible 
to state what types of examples are within the range of 
school work. 

The significant characteristics of these abilities or auto- 
matic responses are the rate or speed of performance and 
the accuracy of the response. Thus, the measurement of 
arithmetical abilities involves determining only at what 
rate a pupil is able to do examples of the elemental types, 
and how accurate his answers are. This is accomplished by 
having him do examples of a given type for a specified time. 



114 MEASURING THE RESULTS OF TEACHING 

From his test paper his rate and per cent of examples cor- 
rect may be determined. These two quantities represent the 
measure of his ability to do this type of example. 1 

Limitations of Series B. A complete and detailed meas- 
urement would require that a test be provided for each 
type of example, but fortunately certain combinations can 
be made. An example in addition consisting of three col- 
umns of nine figures each includes the addition combina- 
tions, simple column addition, and carrying. Thus, if a 
pupil responds satisfactorily to examples of this type, we 
know that he possesses the ability to do the types of addi- 
tion examples involved therein. On the other hand, if his 
response to this type of example is unsatisfactory, we do 
not know just what elemental ability he lacks. The use of 
a single test of this type, such as Series B, to measure a 
group of arithmetical abilities has this very obvious limita- 
tion in diagnosing the conditions which exist, but it does 
provide a very satisfactory general survey. 

Diagnostic Tests. Any series of classroom tests must not 
require a large amount of time if they are to be used by any 
besides the most enthusiastic workers. Thus, in construct- 
ing a series of diagnostic tests in the operations of arithmetic, 
due regard must be had for the amount of time that will be 
required. Bearing this fact in mind the writer has devised 
a series of twenty-one tests which require only thirty-one 
minutes of working time and which it is believed furnish a 
reasonably complete diagnosis of the abilities of pupils to do 

1 Strictly speaking, the number of examples done and the per cent of 
examples correct is a measure of the pupil's performance rather than of his 
ability. A pupil's performance is affected by many factors such as his emo- 
tional status, physical condition, light, temperature, and the like. Or, it 
may be that a pupil does not try to do his best on a given test. A pupil's 
ability can only be inferred from his performance, but when conditions are 
properly controlled, such inference is reliable in all except a few cases. In 
order to avoid an awkward form of statement and because the practice is 
general, we shall speak of a score as a measure of a pupil's ability. 



THE OPERATIONS OF ARITHMETIC 115 

the operations of arithmetic with the exception of the types 
of examples involving mixed numbers and integers with 
fractions. In order to avoid an excessive number of tests it 
has been necessary to include more than one type of exam- 
ple within a single test. When this has been done the differ- 
ent types are closely related and they always occur in rota- 
tion. 

The following samples from each test will illustrate the 
types of examples included in the several tests: 

Addition 
Test I TestV Test VII Test XII Test XV 

4 7862 7 1/6 + l/3 = 1/6 + 3/5 = 

7 5013 6 5/6 + 1/2 = 3/l2 + 5/8 = 

2 1761 6 3/10 + 3/5 = 

5872 5 5/9 + 2/3 = 

3739 

5 

1 
8 
7 
3 
13 
1 
2 1 



Subtraction 

Test II Test IX Test XIII 

37 94 739 1853 3/4-2/5 

5 8 367 948 5/6-3/4 



Muttiplication 

Test III Test VIII Test X 
6572 4857 560 807 617 840 
6 36 37 59 508 80 

Test XIV Test XVIII Test XX 

2/3X3/4 657.2 67.50 487.5 57.28 

2/5 X 3/7 .7 .03 .62 9.5 

5/12X3/5 _ 460Q4 g0250 302250 544160 



116 MEASURING THE RESULTS OF TEACHING 

In Tests XVIII and XX the pupil is simply to insert the 
decimal point in the product which is given. In the samples 
only the variations in the multiplier are given. Each multi- 
plier is used with three types of multiplicands (657 . 2, 65 . 72, 
6.572). Thus each test includes six types of examples. 







Division 




Test IV 




Test VI Test XI 


Test XVI 


8)3840 




82)3854 47)27589 


2/5 4- 1/3 
4/7 -f- 2/3 
3/8 -T- 2/3 


Test XIX 


:37 


Test XVII 


Test XXI 


.4)148 Arts. 


.03)16.2 Ans. :54 


.47)2758.9 Ans. :587 


.9)65.7 Ans. 


:73 


.07)1.82 Ans. :26 


8.2)38.54 Ans. :47 


.6)1.68 Ans. 


:28 

■A3 


.05)^415 Ans. :83 
.06)7.44 Ans. : 


79)36.893 Ans. :467 


.7). 301 Ans. 





Test XI is a composite test involving the four "cases" of 
long division given by Courtis. In Tests XVIII, XIX, and 
XXI the pupil is to write the answer in the proper place 
and insert the decimal point. In Test XXI each of the 
three types of divisor is placed with each of four types of 
dividends thus providing twelve types of examples. 

Marking the test papers and tabulating scores. The test 
papers are marked in the same way as Series B. The scores 
are also recorded in the same way. Detailed directions ac- 
company the tests. 

Standards. Only tentative standards are available for 
these tests and they are likely to be changed somewhat in the 
future. For that reason they are not reproduced here. The 
best available standards are always furnished with the tests. 

Graphical representation. A plan of graphical representa- 
tion which makes very easy the interpretation of the scores 
of this series of tests will be given in the next chapter in our 
consideration of diagnosis. See Figs. 25 and 26. 



THE OPERATIONS OF ARITHMETIC 117 

Summary. In this chapter we have described two series 
of tests for measuring the abilities of pupils to perform the 
operations of arithmetic; Courtis's Standard Research 
Tests, Series B, and Monroe's Diagnostic Tests. The former 
is to be used for general measurement, the latter for diag- 
nostic measurement. In describing these tests we have 
shown that ability to do the operations is specific. In the 
next chapter the meaning of the scores and correctives for 
the defects discovered by using the tests will be considered. 
In Chapter VI tests for measuring ability to solve problems 
will be described. 

QUESTIONS AND TOPICS FOR STUDY 

1. What is a general test? A diagnostic test? 

2. When would you use a general test? A diagnostic test? 

3. What is diagnosis? 

4. How is the median calculated? 

5. What is the "efficiency" of a class? 

6. What are the "dimensions" of abilities to do examples? 

7. What do we mean by saying abilities to do examples are specific? 



CHAPTER V 

DIAGNOSIS AND CORRECTIVE INSTRUCTION IN 
ARITHMETIC 

Purpose of giving standardized tests is to furnish basis 
for improving instruction. As in the case of reading, the 
fundamental purpose of giving standardized tests in arith- 
metic is to secure information which the teacher may use 
in improving the instruction. Series B can be used to secure 
general information concerning the abilities of the members 
of a class. The scores will tell the teacher, for each of the 
four operations, whether his pupils are above or below 
standard in rate of work and in accuracy. With this infor- 
mation at hand, the teacher knows where he should place 
the emphasis in his instruction; that is, whether he is devot- 
ing insufficient time to practice upon the operations, or 
whether the pupils are being drilled when they are already 
up to standard, or whether he should place more emphasis 
upon the rate of work or upon accuracy. 

However, when we recall the nature of ability in the oper- 
ations of arithmetic, it appears that Series B cannot furnish 
as complete information as is necessary for planning details 
of instruction, such as the types of examples which should 
receive emphasis. A more elaborate series, such as Monroe's 
Diagnostic Tests, is necessary. In certain cases it is very 
helpful to supplement the diagnostic tests with an analytical 
diagnosis. 

In this chapter we shall consider (1) the meaning of scores 
obtained by using Series B and the instruction which should 
be given to correct the conditions revealed; (2) the use of the 
Diagnostic Tests and how to use the results; (3) supplemen- 
tary or analytical diagnosis. 



INSTRUCTION IN ARITHMETIC 119 

I. Courtis's Standard Research Tests, Series B 

Type I. Below standard in both rate and accuracy. The 
causes. There is given in Fig. 21 the record of a fifth-grade 
class for the addition test. The standards have been indi- 
cated by drawing heavy lines. The four divisions into which 
these lines divide the record sheet make the interpretation 
of the groups more simple. The records of this class for the 
other three tests are similar, showing that it is rather con- 
spicuously below standard in both rate and accuracy. Sev- 
eral causes for this condition are possible. The pupils may 
not know the tables. They may not have learned a good 
method of work. They may lack sufficient effective drill 
upon these types of examples. In the absence of scientific 
information on this point it is the writer's opinion that the 
last-mentioned cause is the most probable. Saying that the 
most probable cause is insufficient drill does not necessarily 
mean that not enough time has been given to drill. Much 
time may be given to drill and the drill not be effective be- 
cause the teacher uses a poor classroom procedure. 

An illustration of inefficient drill. Frequently the writer 
has visited classes in arithmetic which were being drilled 
upon the fundamental operations. A fairly uniform pro- 
cedure was followed. The same example was dictated to all 
of the pupils, regardless of whether they needed drill upon 
this particular type of example or not. Naturally some 
pupils finished very quickly, and, as they waited for their 
classmates to finish, there was a tendency for them to be- 
come disorderly — a perfectly natural tendency. When a 
majority of the class had finished the example, the teacher 
stopped the work and read the correct answer. The process 
was then repeated. The result was that those pupils who 
worked slowly completed few, if any, examples during the 
entire period, and, therefore, received little satisfactory 





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INSTRUCTION IN ARITHMETIC 121 

drill. The bright pupils spent a considerable portion of 
their time waiting on the other members of the class, and 
probably did not need the particular kind of drill which 
they received. 

Some teachers spend a great deal of time in having exam- 
ples explained by pupils, the explanation consisting merely 
of an oral reproduction of the process of adding, subtract- 
ing, etc. There is a time in the learning process when pupils 
need explanation, but in the operations of arithmetic, after 
they understand what to do, attentive repetition is required. 
This requires an efficient plan of drill. Another point which 
should be noted is that the drill must be upon all the types 
of examples which they are to learn to do and not upon the 
tables or some other single type. 

The remedy. (1) A modified classroom procedure. The 
type of class instruction described on page 120 can easily be 
modified so as to make the drill more efficient and to insure 
that the slow-working pupils will get some satisfactory drill. 
Instead of dictating only one example at a time, the teacher 
can dictate several, and stop the work as soon as a few of the 
faster workers have finished. The slow-working pupils will 
have some examples completed and the faster workers will 
not have been idle. 

{2) Rate of work must be recognized. The teacher must 
recognize that the rate at which the pupil performs the 
operations is important, as well as the accuracy. This means 
that, in teaching, the teacher must obtain a measure of the 
pupil's rate, as well as a measure of his accuracy. If exam- 
ples are dictated in groups, and the work stopped as sug- 
gested in the above paragraph, the number of examples 
which the pupil does during the class period is a measure 
of his rate of working. The per cent correct is a measure of 
his accuracy. 

(3) Motivation, Another means of increasing the scores of 



122 MEASURING THE RESULTS OF TEACHING 

a class is to secure a strong motive for the work. Arithmetic 
is one of the best liked of the drill subjects. This is particu- 
larly true of the operations. This being the case, the moti- 
vation of drill in arithmetic generally is a comparatively 
simple matter, and in most cases it will be sufficient simply 
to start the pupils to work and to keep the work from lag- 
ging. When more than this is necessary, the teacher must 
demonstrate her resourcefulness by providing an effective 
method or device for the motivation of arithmetical drill. 
In the lower grades the playing of certain games provides 
practice upon certain types of examples. In the upper 
grades ciphering-matches, or, better, the setting of definite 
standards in both rate and accuracy, are very effective mo- 
tives. 

Standards used to motivate work in arithmetic. The 
writer has visited classrooms in which the teacher had 
posted a chart giving the median scores of the class at the 
beginning of the school year and the standards which should 
be reached by the end of the year. Teachers testify that 
this is an effective means of stimulating interest. Figures 
in the latter part of this chapter illustrate plans for repre- 
senting the standing of a class on a chart. 

Type H. Below standard in rate with satisfactory accu- 
racy. Sometimes a class will be found with a satisfactory 
median score in accuracy, but conspicuously below standard 
in rate of work. This condition may be due to the fact that, 
through the neglect of the rate of work by the teacher, the 
pupils have not been trained to work rapidly. It may be 
due to the pupils having the habit of applying some check 
to their work or doing it a second time. Some pupils work 
slowly because they are not concentrating their attention 
upon what they are doing. In giving tests the writer has 
observed pupils stop and look around the room or out of the 
window, showing thereby that they were working at a very 



INSTRUCTION IN ARITHMETIC 123 

low pressure. Other pupils have been found to work slowly 
because they have acquired inefficient methods of work. 
One such method which is frequently found is the use of an 
elaborate phraseology or formula in performing the opera- 
tions. (This cause is treated more fully on page 149.) 

The remedy for this type of situation is primarily to place 
more emphasis upon the rate of work in classroom drills. 
The pupils should be given timed drills and judged upon 
the basis of their rate of work as well as the accuracy of their 
results. The modified classroom procedure suggested above 
makes this possible. If pupils have acquired habits of work 
that are undesirable, such as counting on the fingers or 
tapping out sums or repeating the numbers to be added, 
subtracted, etc., they should be corrected. Also a strong 
motive will tend to increase the rate of work. In increasing 
the rate of work, care must be exercised to make certain 
that the pupils do not become inaccurate. However, as in 
the case of silent reading, high rate and high accuracy are 
not incompatible. In fact they frequently go together, and 
frequently an increase in the rate of work in arithmetic is 
accompanied by an increase in accuracy. 

Type HE. Below standard in accuracy with satisfactory 
or high rate. If one takes the position that the only satis- 
factory standard for accuracy is one hundred per cent, this 
case occurs very frequently. If one accepts the general 
medians of Table XIV as satisfactory standards, it occurs 
much less frequently. In this discussion we shall accept the 
general medians as satisfactory standards. A median score 
in accuracy may be below standard because the test was 
given to the pupils in such a way that they became excited 
and worked very rapidly when they were accustomed to 
work slowly. When it is suspected that this is the cause, 
the test should be repeated, using a different form, and exer- 
cising care not to excite the pupils. Pupils should become 



124 MEASURING THE RESULTS OF TEACHING 

accustomed to working under timed conditions by being 
timed in doing the regular class exercises. 

Another reason for a low median score in accuracy may 
be the lack of sufficient practice upon the types of examples 
used in these tests. If this is the cause, the remedy is obvi- 
ous, and the suggestions given above in respect to effective 
methods of drill will apply. 

Type IV. Scores too widely scattered. An illustration is 
given of this type of situation in Fig. 22. The median rate 
of this class is above standard and the median accuracy is 
only slightly below. Thus, as judged by its median scores 
the standing of this class is satisfactory, but the scores are 
not closely grouped about the central tendencies. Although 
the class is relatively small the rates of work vary from four 
examples to seventeen examples and the accuracy scores are 
recorded in each interval of the record sheet. This is an 
illustration of a condition which prevails to some extent in 
practically every class. Unless the class is very small, there 
will be a distribution of scores extending over several inter- 
vals of the record sheet. 

The overlapping of the several grades. When the distri- 
butions of the scores for successive grades are compared, a 
great overlapping is found. Some pupils in the fourth grade 
make higher scores than a number of the eighth-grade pupils. 
Table XV shows the distribution of pupils in a certain city 
according to the number of examples attempted in the sub- 
traction test of the Courtis Standard Research Tests, Series 
B. An examination of the table on page 126 reveals these 
facts : 

In the fourth grade twenty-three per cent of the pupils 
reach or exceed the fifth-grade median. 

In the fifth grade twenty- three per cent of the pupils 
reach or exceed the sixth-grade median. 

In the sixth grade twenty-four per cent of the pupils reach 
or exceed the seventh-grade median. 





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126 MEASURING THE RESULTS OF TEACHING 



Table XV. Showing the Distribution of the Pupils of a 
City according to the Number of Examples Attempted, 
Courtis's Standard Research Tests, Series B 

Subtraction 



Grade 


Number of examples attempted 


1 


2 


3 

11 
3 
1 

1 


4 

17 
9 

2 

1 


5 

19 
10 
8 
2 


6 

18 

IS 
9 
6 


7 

10 

23 

2d 

9 

9 


8 

8 
21 
16 
13 
13 


9 

4 
8 

14 
12 

8 


10 

4 
2 
14 
16 

19 


11 

1 

3 
9 
14 
12 


12 

2 
1 

12 

15 


13 

4 
6 
8 


14 

2 

5 

5 


15 

2 
2 


16 
3 


17 

2 


IS 
2 


19 
1 


20 
1 


Me- 
dian 


IV.. 

v.. 

VI.. 

VII.. 

VIII.. 


1 


7 
1 


5.7 

7.4 

8.6 

10.4 

11.0 



In the seventh grade forty per cent of the pupils reach or 
exceed the eighth-grade median. 

This condition is merely typical. Three causes may be 
given: (1) imperfect classification of pupils; (2) native indi- 
vidual differences in the pupils; and (3) the training which 
they have received. As a rule only a few cases can be 
accounted for on the basis of imperfect classification when 
we remember that except where the school has been depart- 
mentalized, the pupils have been grouped not only for in- 
struction in the operations of arithmetic, but also for in- 
struction in other subjects, and that pupils who are low in 
arithmetic may stand high in some other subjects. Native 
differences remind us that pupils are different and that 
complete uniformity cannot be secured. It is, therefore, 
the third cause which concerns us most. 

The effect of class instruction not suited to all pupils. The 
effect of class instruction is shown when a test is repeated 
after an interval of a few months. In Table XVI the mid- 
year 1 distributions for a certain city on the addition test of 

1 The first test was given just after the midyear promotions. The tests 
were given to about one hundred and fifty pupils in each grade. 



INSTRUCTION IN ARITHMETIC 



127 



Table XVI. The Range of Numbek of Examples Attempted 

(Upper numbers for each grade are for the mid-year test. Lower numbers 
refer to the May test.) 

Addition 



Grade 


Total range 


Range in number 
of examples 


Range of middle 
50 per cent 


Range in 
number of 
examples 


IV 


1-10 
1-17 
2-14 
3-16 
2-12 
4-24 
3-24 
4-24 
4-18 
5-17 


10 
17 
13 
14 
11 
21 
22 
21 
15 
13 


3.6- 5.9 
5.0- 8.3 

4.7- 7.0 

6.8- 9.0 
5.7- 8.4 
7.2-11.0 
6.9-10.0 
8.5-12.3 
8.1-10.8 
8.9-12.1 


2.3 


V 


3.3 

2.3 


VI 


2.2 
2.7 


VII 


3.8 
3.1 


vni 


3.8 
2.7 




3.2 



Series B are compared with those for May. With only two 
exceptions both the total range of the scores and the range 
of the middle fifty per cent were increased. This fact shows 
that the instruction in addition which these pupils received 
was more appropriate for the brighter pupils than for those 
who were below standard ability. Some pupils acquired 
abilities far in excess of the standards for their grade, while 
others remained conspicuously below the standard. This is 
merely what we should expect, because those pupils who 
have profited most under the system of instruction may be 
expected to continue to profit most. Obviously, if our stand- 
ards are wisely determined, the pupils who are below stand- 
ard in ability need instruction and those who are conspicu- 
ously above standard may spend their time more wisely 
upon other subject-matter. If this is not feasible, the 
methods and devices of instruction should be those most 



128 MEASURING THE RESULTS OF TEACHING 

appropriate to those pupils who are below standard. If the 
methods of instruction are unchanged, it is obvious that the 
pupils who have learned most readily will continue to do so. 

The bright pupil should receive consideration as well as 
the backward pupil. The usual class instruction does not 
give the bright pupil efficient training. He is not forced to 
exert himself. Much of the time he is forced to be inactive. 
Furthermore, in the case of the tool subjects (the operations 
of arithmetic, reading, spelling, handwriting, and language), 
training beyond a certain point is not very profitable. In 
arithmetic the bright pupil should be given problem work 
rather than additional training upon the operations. 

The remedy. Where reclassification of the pupils is pos- 
sible and appears wise in the light of the achievements of the 
pupils in other parts of arithmetic and in their other sub- 
jects, a closer grouping can be secured by promoting those 
who are conspicuously above standard. Some may be put 
back a grade. But it will be found that many pupils will be 
below standard only in certain items. To handle these cases, 
individual, or at least group, instruction is required, because 
it is obvious that all members of the class do not need the 
same instruction. Before individual instruction can be 
wisely planned, additional information concerning the mem- 
bers of the class is needed. This may be secured (1) by using 
diagnostic tests and (2) by analytical diagnosis. We shall 
therefore treat Type IV more fully under the head of 
Diagnostic Tests. 

Type V. Irregular development. Fig. 23 shows the median 
scores of two classes in a certain city. In the number of 
examples attempted, Class A is nearly three examples higher 
in subtraction and multiplication than in addition. Class B 
has very high scores in addition, but lower ones in the other 
operations, particularly multiplication and division. The 
relative position of the line showing the median number of 



INSTRUCTION IN ARITHMETIC 



129 



14 



13 



12 



II 



10 



examples right shows Class A to be inaccurate in all opera- 
tions except division, where perfect or one hundred per cent 
accuracy is indicated. On the other hand, Class B, which in 
general is relatively 

very accurate in * 5 AW . sxA . 

the other operations 
does not attain per- 
fect accuracy in di- 
vision. Such irregu- 
lar or uneven de- 
velopment is not 
unusual. It is more 
frequent and more 
pronounced in indi- 
vidual pupils than 
in classes. 

In Fig. 24 we 
show the records of 
a girl who was tested 
twice with Series B, 
first, as she was fin- 
ishing the seventh 
grade and again as 
she was completing 
the eighth grade. 
In the figure her 

records are indicated by broken lines and the position of 
the eighth-grade standards (Boston) are shown by the solid 
line. In the seventh grade this girl's development was ir- 
regular. In subtraction she had fourth-grade ability (see 
Table XIV), and in addition she was about fifth-grade. In 
division she was above eighth-grade ability. 

Such uneven development in either a class or an individual 
pupil is probably caused by not properly distributing the 



A 


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_ B 


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Fig. 23. Showing Median Scores op Two 
Classes in the Same City. (After Ash- 
baugh.) 



INSTRUCTION IN ARITHMETIC 131 

drill. A study of the median scores of a class on the several 
tests of the series will tell the teacher where the most 
emphasis should be placed in the class instruction. A study 
of the records of a pupil will furnish information for planning 
individual instruction. In Fig. 24 the broken line drawn for 
the eighth-grade scores shows that the development of this 
pupil was evened up during that grade. Such complete 
evening-up of scores is unusual, but if the teacher places 
emphasis upon the operations in which low scores are made 
marked improvement will result. 

II. Monroe's Diagnostic Tests 

More detailed information is secured by using diagnostic 
tests. An illustration of the irregular development of a class. 
By using the diagnostic tests described on page 114, more 
detailed information can be secured concerning a class or a 
pupil. In Fig. 25 the median scores of three sixth-grade 
classes in one city are represented. The plan of graphical 
representation is similar to that used in Fig. 7. The two 
scores of a test are represented on the sides of an elongated 
rectangle, the number of examples attempted on the upper 
side and the number right on the lower side. The scale on 
each line has been chosen so that the standard scores of 
the twenty-one tests for a given grade fall on a straight 
vertical line. Thus the sixth-grade standards all lie on 
the vertical line drawn from VI, seventh-grade standards 
on the vertical line drawn from VII, etc. The scale on the 
lines has been omitted in order to prevent the crowding 
of the figure. The numbers and letters at the left of the 
figure give the number of the test and the operation. 

Series B has been used for several years in the city from 
which the sixth-grade records shown in Fig. 25 were taken, 
and we may therefore assume that conditions are as good 
or possibly better than in the average city. Classes A and 



132 MEASURING THE RESULTS OF TEACHING 




Fig. 25. Showing the Median Scores op Three Sixth-Grade 

Classes. 



B have thirty-three pupils each and Class C twenty-three 
pupils. The figure shows two significant facts: (1) certain 
points of non-uniformity between the medians of the three 



INSTRUCTION IN ARITHMETIC 133 

classes, and (2) the non-uniform abilities of any one of the 
classes. 

In certain of the tests, such as 2, 6, 8, 15, 18, and 20, the 
median scores of three classes fall within an interval of about 
one grade. In others, notably Tests 13 and 21, the extreme 
difference is much greater. Evidently the teachers of the 
different classes have not been placing equal emphasis upon 
the different types of examples. Take, for example, the addi- 
tion tests (1, 5, and 7). The teacher of Class B has been 
placing much emphasis upon the type of example in Test 5 
(short-column addition with carrying), although it should 
be noted that she has not neglected the other types of ad- 
dition examples. On the other hand, the teacher of Class 
C has neglected short-column addition (Test 1), while the 
teacher of Class A has given much emphasis to it. In Test 7 
there are represented three degrees of emphasis. 

The non-uniform character of the abilities of a class is 
very obvious from the irregularity of the lines representing 
their abilities. Perfect uniformity would be represented by 
a straight vertical line. The non-uniformity in the abilities 
is due to the failure of the teacher to place the appropriate 
degree of emphasis upon the several types of examples. 
Some types doubtless require more emphasis than others, 
and it is the teacher's problem (or is it the problem of the 
maker of the course of study?) to determine the degree of 
emphasis which is needed for each type. 

An illustration of the irregular development of pupils in 
the same class. In Fig. 26 there are shown the scores of 
three sixth-grade pupils selected almost at random from 
Class A in Fig. 25. H. H. is a twelve-year-old boy, H. C. a 
ten-year-old girl, and D, H, a girl, age not given. One 
should expect greater variations when dealing with the scores 
of individual pupils, but the variations of these scores must 
be surprising to one who has not studied the subject. Each 



134 MEASURING THE RESULTS OF TEACHING 




Fig. 26. Showing the Individual Scores of Three Sixth-Grade 
Pupils in the Same Class. 

Class A in Fig. 25. 

of these pupils has scores on certain tests conspicuously be- 
low the standard for the fourth grade and on other tests 
has scores conspicuously above eighth-grade standards. 



INSTRUCTION IN ARITHMETIC 135 

Since these pupils were members of the same class, they 
had probably received the same instruction, and yet the 
instruction which had been sufficient for one had not always 
been satisfactory for the others. Pupils differ in the instruc- 
tion which they need. The instruction which will cause one 
pupil to learn may make no impression on another. 

Arithmetic a complex subject. The facts described above 
show that the product of arithmetical instruction is com- 
plex, much more complex than teachers and supervisors gen- 
erally realize. The fact that the scores obtained by using 
these tests show such great variations in the relative degree 
of ability in the different types of examples, when the pupils 
have been measured with the Courtis Standard Research 
Tests, Series B, at regular intervals, is evidence of the need 
which exists for a series of diagnostic tests. Teachers are 
probably failing to place the appropriate degrees of empha- 
sis upon the different types of examples, because they are 
ignorant of what types exist, or do not know the degree of 
ability which has been attained by their class, and much 
less the degree of ability attained by the individual pupils. 
A series of diagnostic tests, such as described in chapter IV, 
are valuable to the teacher in two ways: (1) as a statement 
of the important types of examples, and (2) as an instru- 
ment for diagnostic measurement. 

An illustration of individual instruction. To correct the 
individual defects individual instruction is needed. A 
teacher can fit his instruction in the operations of arith- 
metic to the needs of his pupils by preparing a number of 
sets of examples, each set being confined to examples of the 
same type. These sets of examples should be written on 
cards. Then, instead of dictating examples, the teacher can 
distribute the cards and have the pupils copy the examples 
from the cards. If the teacher studies the needs of his 
pupils, it will be possible for him to distribute the cards so 



136 MEASURING THE RESULTS OF TEACHING 

that each pupil will have the type of example upon which 
he needs practice. The pupil is probably injured by being 
required to practice upon the wrong type of example, and, 
hence, it is very important that each pupil be given the type 
of example upon which he needs practice. 

The Courtis Standard Practice Tests used for individual 
instruction. Courtis has devised a set of Standard Practice 
Tests, l which automatically diagnoses each pupil and fur- 
nishes the practice which he needs to remedy his defects. 
These tests consist of forty-eight sets of exercises, which 
"have been designed to cover every known difficulty in the 
development of ability in the four operations with whole 
numbers." The latest form of these tests (1916) is arranged 
so that the pupils begin the series by taking Lesson 13, a 
test involving all types of examples found in the first twelve 
lessons. 2 All pupils who attain standard ability on this test 
are excused from the first twelve lessons, because they have 
demonstrated that they do not need the instruction which 
these lessons provide. As soon as a pupil who did not attain 
standard ability on Lesson 13 has finished the first twelve 
lessons, he takes Lesson 13 again to show that he is now up 
to standard. Lessons 30, 31, and 44 are also test lessons, 
and are used in the same way. 

Each of the lessons is printed upon a card and a copy is 
furnished to each pupil. The card is placed beneath a sheet 

1 Full details regarding these tests may be obtained from the publishers, 
World Book Company, Yonkers, New York, and Chicago, Elinois. 

Another series of exercises, known as the "Studebaker Economy Practice 
Exercises," and based upon some of the same general principles, has been 
devised by J. W. Studebaker, Assistant Superintendent of Schools, Des 
Moines, Iowa. They are published by Scott, Foresman & Company, New 
York and Chicago. Other series of practice exercises have been devised, 
but, so far as the writer has examined them, they are less complete and give 
less promise of efficient means of instruction. 

2 All lessons except the test lessons are confined to a single type of 
example. 



INSTRUCTION IN ARITHMETIC 137 

of transparent paper and the example is read through the 
paper, the work being done on the paper. The lessons have 
been constructed so that the standard length of time re- 
quired to complete each one is the same. They are also self- 
scoring. These two features relieve the teacher of the labo- 
rious work of scoring the papers, and make it possible for 
different pupils to be working upon different lessons at the 
same time. Thus, when a pupil has demonstrated that he is 
up to standard on any type of example, he may at once go 
on to the next lesson. If he is not up to standard on any 
lesson, his work makes the fact obvious, and he can remain 
upon that lesson until he acquires the necessary ability 
without interfering in the least with the work of the other 
members of the class. 

Thus, individual progress is provided for, and at the same 
time the group formation is retained. A considerable saving 
of pupils' time is effected by excusing from drill those pupils 
who demonstrate that they possess standard ability. These 
pupils can spend this time upon other work. 

The use of the Standard Practice Tests in ungraded 
schools. These Standard Practice Tests also simplify in- 
struction in ungraded schools. In fact they save more time 
there than in graded schools. The same lessons are used for 
all pupils in Grades four to eight. Only the time allowed 
differs. Thus, all of the pupils in a rural school could be 
instructed at the same time and each pupil receive the prac- 
tice which he needed. 

The most important thing. However, it must not be for- 
gotten that any set of practice exercises is merely a teaching 
device. It is more important that the teacher explicitly 
recognize in her thinking that she is instructing a group of 
pupils who differ widely in native ability, experience, and 
training, that all do not learn in the same way, and that a 
limitation should be placed upon training. When she ex- 



138 MEASURING THE RESULTS OF TEACHING 

plicitly recognizes these facts, the resourceful teacher will 
find many devices which will be helpful in adapting the in- 
struction to the needs of the pupils. 

III. Analytical Diagnosis 

The need for analytical diagnosis. Diagnostic tests, and 
to a lesser degree general tests such as Series B, locate defects 
in classes and in individual pupils, but they do not tell the 
teacher the cause of the defect. The knowledge of the exist- 
ence of the defect is very helpful to the teacher and she can 
proceed to eliminate it by increasing the amount of practice 
or by other devices as has been suggested in the preceding 
pages. Many cases will be corrected by such treatment, but 
some will not for the reason that the cause of the defect has 
not been removed. 

The method. Whenever a pupil is found to be conspicu- 
ously below standard, the cause should be sought by "ana- 
lytical diagnosis." This kind of diagnosis includes three 
types of procedure: (1) observing the pupil as he works; 
(2) studying his test papers; (3) having him do the examples 
orally. 

Defects discovered by observing the pupil as he works 
under normal conditions. Courtis 1 recommends this method 
of diagnosis and lists seven possible symptoms for addition: 

1. Child's movements very slow and deliberate, but steady. 

2. Child's movements rapid, but variable. Adding accompanied 
by general restlessness, sighs, frowns, and other symptoms of 
nervous strain. 

3. Child's progress up the column irregular; rapid advance at 
times with hesitation, or waits, at regular or irregular intervals. 
Often gives up and commences a column again. 

4. Child stops to count on fingers, or by making dots with pen- 
cil, or to work out in its head the addition of certain figures. 

1 Courtis, S. A., Teacher s Manual for Hie Standard Practice Tests (World 
Book Company, 1915), pp. 16 ff. 



INSTRUCTION IN ARITHMETIC 139 

5. Child adds each first column correctly, but misses often on 
second and third columns. 

6. Child's time per example increases steadily or irregularly, 
particularly after two or three minutes' work; i.e., 15 seconds each 
for first five examples, 17 seconds each for the next five, 23 seconds 
for next two, 45 seconds for the next example, etc. 

7. Child's habits apparently good and work steady, but answers 
wrong. 

Methods of correcting these defects. Courtis recommends 
the following correctives for these defects: 

1. Slow movements may be due either to bad habits of work or 
to slow nerve action. In the latter case, the difficulty will prove 
very hard to control. It is almost certain that no amount of train- 
ing will ever alter the nerve structure and so remedy the funda- 
mental cause. But in all such cases much can be done to generate 
ideals of speed, to help the child to eliminate waste motions, and 
to hold himself up to his best rate. 

In any case the procedure would be as follows : Ask the child to 
add the first example alone so that you may time him. Give him 
the signal when to start and let him signal when he has finished. 
Let him make several trials of the same example to make sure that 
he does not improve under practice. The teacher should then give 
the child the watch and let him time the teacher in working the same 
example. Comment on difference in child's and teacher's times. 
Then have the child write in small figures all the partial sums, as 
shown in the illustration. The teacher should again time the child, 
letting him read to himself the partial sums as rapidly as 
he can. This will, of course, give the minimum time in 30 46 15 
which the child could possibly add the example. The 26 41 9 
time records of a child with true defective motor control ^97 8 
will show slight improvement, if any, even with such aid, 13 60 
and probably the only procedure to follow in such cases 7 61 
is to lower the standard to correspond. Where there is 
a marked difference in time between the original and this last 
performance, the child will get, for the first time in its life, per- 
haps, a perfectly clear conception of what working at standard 
speed really means, as well as the sensation of really working at 
that speed. The teacher and child should then practice the same 
example over and over until the child can without the crutches add 



140 MEASURING THE RESULTS OF TEACHING 

it at the standard rate. Now the teacher can give him the whole 
test again, urging him to work at his best speed and comparing 
his results with the first result. The improvement made by ten 
minutes of this kind of work enables the teacher to say that a 
proper amount of similar study would produce the changes de- 
sired. 

But, some teacher will say, "Will the child not learn the exam- 
ple by heart?" This is precisely what is desired. A perfect adder 
has learned so many examples "by heart" that it is impossible to 
make up any arrangement of figures that will be in any way new 
to him. The child in the same way needs to perfect his control over 
each example until he finally attains to mastery over all. 

2. If the child gives evidence of nervous strain, check his speed, 
teach him to relax and to work easily and quietly. Get good habits 
of work first, then bring up speed and accuracy by degrees. The 
nervousness of a child is usually caused by social conditions, phys- 
ical health, or temperamental bias. In any event, it is difficult to 
control. Look out for a large fatigue factor in nervous children. 

3. Irregular speed up the column may be due to either of two 
factors: lack of control of attention, or lack of knowledge of the 
combinations. The latter factor will be discussed in the following 
paragraph (4). Attention will be considered here. 

There is a limit to the length of time that a person can carry on 
any mental activity continuously. As time goes on, the mind tends 
to respond more and more readily to any new mental stimulus than 
it does to the old. The mind "wanders," as it is said. The attention 
span for many children is six additions, for some only three or four, 
for others, eight, or ten, and so on. That is, a child whose attention 
span is limited to six figures may add rapidly, smoothly, and accu- 
rately, for the first five figures in the column, giving its attention 
wholly to the work. As the limit of its attention span is reached, 
however, it becomes increasingly difficult for it to concentrate its 
attention. The child suddenly becomes conscious of its own phy- 
sical fatigue, of the sights and sounds around it. The mind balks 
at the next addition; it may be a simple combination, as adding 2 
to the partial sum, 27, held in mind. It finally becomes imperative 
that the child momentarily interrupt its adding activity and attend 
to something else. If this is done for a small fraction of a second, 
the mind clears and the adding activity will go on smoothly for a 
second group of six figures, when the inattention must be repeated. 

It should be evident that these periods of inattention are critical 



INSTRUCTION IN ARITHMETIC 141 

periods. If the sum to be held in mind is 27, there is great danger 
that it will be remembered as 17, 37, 26, or some other amount, as 
the attention returns to the work of adding. The child must, there- 
fore, learn to "bridge" its attention spans successfully. It must 
learn to recognize the critical period when it occurs, consciously to 
divert its attention while giving its mind to remembering accu- 
rately the sum of the figures already added. This is probably best 
done by mechanically repeating to one's self mentally, "twenty- 
seven, twenty-seven, twenty-seven," or whatever the sum may be, 
during the whole interval of inattention. Little is known about the 
different methods of bridging the attention spans and it may well 
be that other methods would prove more effective. The use of the 
device suggested above, however, is common. 

Giving up in the middle of a column and commencing again at 
the beginning is almost a certain symptom of lack of control of the 
attention. On the other hand, mere inaccuracy of addition (as 27 
plus 2 equals 28) may be due to lack of control over the combina- 
tions. If the errors occur at more or less regular points in a column, 
and if, further, the combinations missed vary slightly when the 
column is re-added, the difficulty is pretty sure to be one of atten- 
tion and not one of knowledge. 

4. Hesitation in adding the next figure, when not due to atten- 
tion, is usually due to lack of control of the fundamental combina- 
tions. In such cases, however, the hesitation or mistakes are usu- 
ally repeated at the same point on subsequent additions. The 
teacher should understand that it "takes time to make mistakes," 
and whenever a lengthening of the time interval occurs, it is a 
symptom of a difficulty which must be found and remedied. 

In this case the remedy is not sl study of the separate combina- 
tions. It has been proved ! that for most children time spent in 
study of the tables is waste effort; that the abilities generated are 
specific and do not transfer. A child may know 6 plus 9 perfectly, 
and yet not be able to add 9 to 26 in column addition except by 
counting on its fingers. The combinations must be learned, of course, 
but they should be learned by practicing column addition. Follow the 
method outlined in paragraph (1) above, having the column added 
over and over again until both standard speed and absolute accu- 
racy have been attained. 

1 See Bulletin no. 2, Department of Cooperative Research, Courtis 
Standard Tests, 82 Eliot Street, Detroit, Michigan. Price 15c. See also 
Journal of Educational Psychology, September, 1914. 



142 MEASURING THE RESULTS OF TEACHING 

5. The sums of a child who is unable to remember the numbers 
to be carried, but whose work is otherwise perfect, will usually have 
the first column added correctly, as well as all single columns. 
Unfortunately, however, inability to carry correctly is usually a 
fault of children with weak memories for partial sums in the col- 
umn. It is well, therefore, to test the carrying habits of any child 
that is inaccurate. Many children do not add the number carried 
until the end of the next column; it should, of course, be added to 
the first figure in the column. If necessary the number to be carried 
should be emphasized as by saying, when the sum of a column is 27, 
"carry 2" to one's self as the 7 is written. This is again a time- 
consuming device which should be adopted only as a last resort. 
The carrying should be an automatic, unconscious operation. Re- 
peated practice on a few examples until the same become so per- 
fectly familiar that a child's whole attention may be given to es- 
tablishing correct habits of carrying will prove beneficial. 

6. Marked increases in the times required for the successive ex- 
amples of a test are an indication of a fatigue factor in the control 
of the attention. Some children are unable to carry on continu- 
ously a single activity, as adding, through even a four-minute time 
interval without a very great loss in power. Two courses are open 
to the teacher, one or the other of which is sometimes effective: one 
is to determine the exact length of the interval at which the child 
can work efficiently, and then try to extend the interval slightly 
each day; the other is to set the child at work on very long and 
very hard examples, and to lengthen the time intervals to fifteen 
or twenty minutes' continuous work. Difficulties of this type are 
hard to remedy. 

Errors discovered by examining test papers. This method 
of diagnosis cannot always be used because some examples, 
e.g., the addition test of Series B, are such that the nature 
of the pupil's errors cannot be determined from his work. 
However, in common fractions and to a certain extent in 
subtraction, multiplication, and division of integers, the 
nature of the errors can be determined. 

An illustration of errors made on Series B. Gist 1 exam- 

1 Gist, Arthur S., "Errors in the Fundamentals of Arithmetic"; in 
School and Society (August 1J, 1917), vol. 6, p. 175. 



INSTRUCTION IN ARITHMETIC 



143 



ined 812 papers of the Courtis Standard Research Tests, 
Series B, chosen at random from six schools in Seattle. The 
frequency, reduced to a per cent basis of each type of error 
for subtraction, multiplication, and division in the respec- 
tive grades, is shown in Table XVII. In subtraction "omis- 
sions " refer to the number of pairs of digits omitted alto- 
gether. Reversions occur when 9 should have been taken 
from 8, but the digits were reversed. The error indicated 
by 7-0, is only typical of many similar mistakes when a 
cipher occurs. The left-hand digit caused some trouble in 
the eighth grade. In the example: 

107795491 
77197029 
129598462 
the left-hand digit was carried down, as shown. 



Table XVII. Frequency of Types of Errors nsr Subtraction, 
Multiplication, and Division, based upon a Study of 812 
Test Papers, Courtis's Standard Research Tests, Series B. 
(Gist.) 



Subtraction : 

Borrowing 

Combinations 

Omissions • 

Reversions 

7-0, etc 

Left-hand digit 

Multiplication : 

Tables 

Addition 

Cipher in the multiplier 

Division : 

Remainder too large 

Multiplication 

Subtraction 

Last remainder and in the dividend 

Multiplicand larger than the dividend 

Failure to bring down all of the dividend.. 

Failure to bring down correct digit 

Failure to place all of quotient in quotient 
Cipher in quotient as 908-98 



4th 5th 6th 7th 8th 



79 
18 
1.5 



52 

45 
2 

1/2 

1/2 





144 MEASURING THE RESULTS OF TEACHING 

Errors in adding common fractions. The errors which 
pupils make in the addition of two fractions have been 
studied so that we know what types are most likely to occur. 
(1) Counts 1 found in a study of tests given to eighth-grade 
pupils that sixty per cent of the errors were due to adding 
the numerators for a new numerator and also adding the 
denominators for a new denominator, as 3/5 + 1/5 = 4/10, 
or 1/9 + 5/9 = 6/18. It will be noticed that these exam- 
ples constitute one of the simplest cases in addition of frac- 
tions. (2) Twenty-seven per cent of the errors were due to 
multiplying the numerators for a numerator and multiplying 
the denominators for a new denominator; as 3/5 + 1/5 = 
3/25, or 1/9 + 5/9 = 5/81. (3) In a test where it was 
necessary to reduce the sum to the lowest terms and to a 
mixed number, Kallom 2 found that nineteen per cent failed 
to reduce the result to a mixed number and eighteen per cent 
failed to reduce it to its lowest terms. About half of these 
pupils failed to make either reduction. About one pupil in 
twenty failed to express the result correctly when reducing 
a fraction to its lowest terms, writing 20/15 = 1 5/15 = 
1/3, instead of 1 5/15 = 1 1/3. (4) Kallom also found 
certain methods of addition which waste the pupil's time 
and tend to introduce errors: 

Approximately one third found it necessary to reduce the frac- 
tions to a common denominator in the first test when the fractions 
were already similar. Some of these children wrote the fractions 
over a common denominator, using for a common denominator the 
denominator of the similar fractions. Others, not noticing that the 
fractions already had a common denominator, used some multiple, 

1 Counts, George S., Arithmetic Tests and Studies in the Psychology of 
Arithmetic (Supplementary Educational Monographs, no. 4, University of 
Chicago Press), p. 65. 

2 Boston Document no. 3. (1916.) Arithmetic; Determining the Achieve- 
ment of Pupils in the Addition of Fractions. Bulletin no. 7 of the Depart- 
ment of Educational Investigation and Research, p. 19. 



2)8 - 


16 


2)4 - 


8 


2)2 - 


4 


2)1 - 


2 



INSTRUCTION IN ARITHMETIC 145 

making necessary reductions. For example, many children added 
3/14 and 1 /14 by reducing the fractions to a common denominator 
of 196. In many cases they then made errors in their work, thus 
obtaining an incorrect answer to the example. Even if carried 
through correctly, this is an ineffective and wasteful way of doing 
such examples. 

Another method used by many individuals consisted of finding the 
least common denominator of such fractions as 1/8 and 3/16 by 
finding the least common multiple of the denominators by short 
division as taught in many of the arithmetics. In such cases the 
following was found: 



2X2X2X2= 16 



1-1 

Errors in subtracting common fractions. Counts found 
two errors which occurred very frequently in subtracting 
fractions having like denominators. (1) Numerators sub- 
tracted for the new numerator and the denominators sub- 
tracted for the denominator as 6/9 — 4/9 = 2/0, or 
3/7 — 1/7 = 2/0. (2) Numerators multiplied for the new 
numerator and the denominators multiplied for the de- 
nominator as 6/9-4/9 = 24/81, or 3/7- 1/7 = 3/49. A 
considerable number of pupils added when subtraction was 
indicated by a minus sign. This may have been due in 
part to the fact that both addition and subtraction were 
included in the same test, but the writer has found sim- 
ilar errors when the two operations were in separate tests. 

Correctives for these errors. The first essential for the 
correction of a defect in a pupil is the knowledge of its 
existence and nature. Without this knowledge attempts to 
correct it must be a random trying of methods and devices 
in hopes that some one will meet the need. Frequently the 
teacher who knows just what defects exist will be acquainted 



146 MEASURING THE RESULTS OF TEACHING 

with some method or device which will serve as an effective 
corrective. If he is not, a knowledge of the laws of habit 
formation, which is the type of learning involved in the 
operations of arithmetic, will help. 

The laws of habit formation. Stated in psychological 
terms, the first law is that in the beginning the attention of 
the learner shall be focalized upon the habit to be acquired. 
In terms of schoolroom practice this means that the learner 
shall understand what reaction is to be made to a given 
stimulus, and shall then react to it in the appropriate man- 
ner. This gives the learner the right start. 

The second law is that the accomplishment of the step 
outlined in the first law shall be followed by attentive repe- 
titions. It is not sufficient that there be simply repetitions 
or drill. The drill must be attentive. In the case of the 
operations of arithmetic this drill may be detached from the 
solving of problems, or it may be given in the solving of 
problems. 

The third law states that no exception shall be permitted 
until the habit is firmly established, which means that the 
attentive practice must be continued until the operation 
has become a habit; that is, has been made automatic. 

"Borrowing." Table XVI shows that, for the pupils of 
Seattle, "borrowing" is the most frequent error in subtrac- 
tion. Some teachers insist that this error can be corrected 
by using the Austrian or additive method of subtraction 
instead of the traditional or " take away " method. Although 
we do not have enough information in order to be able to 
say positively which method is superior, it appears that 
the " take away " method is superior to the Austrian method. 
The latter method may be helpful to certain pupils who have 
difficulty with subtraction. There are two types of errors 
in connection with "borrowing." (1) A pupil may fail to 
" borrow " when he should. (2) '* Borrowing " may become a 



INSTRUCTION IN ARITHMETIC 147 

mechanical feature of subtracting and the pupil will " bor- 
row " when the example does not require it. In the first case 
the pupil must be taught to "borrow." If he has difficulty 
in grasping the idea, the additive or Austrian method may be 
presented. It may be that the first law of habit formation 
has been fulfilled and the pupil needs "attentive repeti- 
tion" or drill. It will also be helpful to have the pupil do an 
example several times before proceeding to another. In the 
second case it will be helpful to give some examples in which 
no "borrowing" is required. This will demonstrate to the 
pupil that " borrowing " does not always occur in subtraction. 

Combinations or tables. Errors in combinations were next 
to "borrowing" in frequency, and errors in tables stand at 
the top of the list in multiplication. Such errors may occur 
because the pupil does not know certain combinations or 
because he does not know them well enough. That is, the 
defect may occur in either the first or second law of habit 
formation. A few pupils have great difficulty in learning 
certain combinations. When this is known to be the case, 
these combinations should be singled out and be made a 
matter of special drill. Generally when errors in the tables 
occur in the fourth grade and above, the combinations 
should not be practiced upon separately, but as they occur 
in examples. The situation is the same as in addition. (See 
page 141.) 

Remainder too large in division. Outside of errors in 
multiplication and subtraction this is the most frequent 
error in division. This error, as well as most of the other 
errors fisted for division, is due to an imperfect plan of 
procedure; that is, to the failure to apply simple checks at 
certain steps of the work. The process of division is peculiar 
in that it is possible to avoid most errors by applying simple 
checks at certain stages of the work, and pupils should be 
definitely taught to do this. It is very simple to note whether 



148 MEASURING THE RESULTS OF TEACHING 

the remainder is too large by comparing it with the divisor, 
and this comparison should be taught as a regular step of 
division. 

Failure to reduce sum in addition of fractions. This error 
is also due to an imperfect routine. Pupils should be taught 
that the reduction of the answer to a mixed number and to 
lowest terms is always a part of the work when possible. 
These errors can be corrected in most cases by the teacher 
insisting that the reduction be made and providing practice 
in doing it. Practice upon reduction apart from addition 
will not be as effective as practice on it as a part of addition. 
It is a good plan to give no credit for work which is not com- 
plete, for the third law of habit formation, permit no excep- 
tions, applies here. 

Incorrect methods in handling fractions. Doing such 
things as adding the denominators when adding fractions is 
due to the pupil having not fixed the procedure for addition. 
To correct such defects, the pupil should be shown the cor- 
rect procedure and drilled upon it. This drill should at first 
be upon only one type of example, but later lists of mixed 
types should be used. Here is a good opportunity to use lists 
written on cards which may be distributed. This makes it 
convenient to time the pupils, and this is very important 
because it requires the pupil to decide quickly upon the 
method to use. 

Time-wasting methods. Kallom (p. 144) reports a num- 
ber of pupils using methods which require more time than is 
necessary. This will be corrected to a large extent by the 
teacher emphasizing the rate of work as being important. 
Of course, it is more important that a pupil have his work 
correct than to work rapidly, but frequently it is helpful to 
emphasize the rate of work. 

Analytical diagnosis by the oral method. By having a 
pupil do examples orally, it is possible to discover (1) par- 



INSTRUCTION IN ARITHMETIC 149 

ticular errors in the combinations and (2) imperfect and 
wasteful methods. 

Illustrations of wasteful methods. By using this method 
of diagnosis the writer has found that in addition many 
pupils repeat each number to be added. For example they 
say, "7 and 6 are 13 and 5 are 18 and 4 are 22 and 5 are 
27," instead of simply calling the partial sums, as "13, 18, 
22, 27." Similar elaborate phraseology is used in the other 
operations. No error is involved in this method, but it 
consumes time. 

UhTs oral diagnosis of errors. Using Lesson 1 of the 
Courtis Standard Practice Tests, which consists of single- 
column addition, three figures to the column, Uhl * studied 
the errors of pupils by having them do the examples orally 
and by asking them detailed questions when their method 
was not made clear. To illustrate the method and also the 
nature of the defects revealed we quote from his report : 

The findings as to methods employed by pupils in "difficult" 
combinations is both interesting and significant. The following 
methods were found in the work of pupils who were tried out in the 
manner just described. A fourth-grade boy showed by slow work 
that the combination 9-7-5 was difficult for him. When ques- 
tioned, he showed that he used a common form of "breaking-up" 
the larger digits. In working the problem, he said to himself: 
"9 + 2 + 2 + 2 + 1 = 16 and 21." This shows that the 9-7 com- 
bination was not known, but that the 16-5 combination was, in- 
asmuch as he arrived at "21" directly after having combined the 
other two numbers. Another boy of the same grade showed the 
same type of difficulty in a more pronounced form. He added 8, 6, 
and as follows: "First take 4, then take 2, then add 8 and 4 makes 
12, and 2 makes 14." In adding 9, 7, and 5 he said: "9 and 3 is 12 
and 4 is 16 and 2-18; and 2-20; and 1-21." He broke into parts 
even so easy a problem as 3 4~ 4 -f- 9, adding 9 + 3 +2 + 2 = 16. 

1 Uhl, W. L., "The Use of Standardized Materials in Arithmetic for 
Diagnosing Pupils' Methods of Work"; in Elementary School Journal 
(November. 1917), vol. 18, p. 215. 



150 MEASURING THE RESULTS OF TEACHING 

A pupil from the fifth grade presented a quite different method 
of adding. In adding 4, 9, and 6 she explained: "Take the 6, then 
add 3 out of the 4. Then 9 and 9 are 18, and 1 are 19." Other 
problems were worked out similarly: one containing 3, 9, and 8 was 
solved as follows: "8 and 8 are 16 and 3 are 19 and 1 are 20"; 5, 6, 
and 9 as follows: "6, 7, 8, 9, and 9 are 18 and 2 are 20." This tend- 
ency to build up combinations of 8's or 9's continued in the case of 
another problem: 6, 5, and 8 were added thus: "6, 7, 8, and 8 are 
16 and 3 are 19." Probably her first problem was worked similarly, 
but I had to have her dictate her method twice before I understood; 
she then gave it as quoted. 

Methods which are quite as clumsy are found in the case of sub- 
traction. One boy of the fifth grade was found to build up his sub- 
trahend in the case of many problems. For example, in subtracting 
8 from 37, he increased his subtrahend to 10, then obtained 27, and 
finally added 2 to 27 to compensate for the addition of 2 to 8. Like- 
wise, in subtracting 7 from 30, he added 3 to 7 and proceeded as 
before. This boy knew certain combinations very well, but did 
problems containing other combinations by a method much harder 
than the correct one. 

Even greater resourcefulness was shown by a fifth-grade boy 
who found the differences between some numbers by first dividing, 
then noting the remainder or lack of one, then multiplying, and 
finally adding to or taking from the result as necessary. For ex- 
ample, in subtracting 9 from 44, he proceeded as follows: "Nine 
goes into 44 five times and 1 less; 4 times 9 are 36, minus 1 equals 
35." That is, this boy knew certain multiplication combinations 
better than he did certain subtraction processes; therefore, he used 
multiplication, making adjustments either upward or downward 
as demanded by the problem. 

The Remedy. Where a pupil simply uses an elaborate 
phraseology he should be trained to use a simplified method. 
The plan of timing the pupil and then having the pupil time 
the teacher, or comparing his rate with the standard rate, 
will show him that his method is slow. The use of such 
methods as described above in the earlier grades may be 
justified, but teachers should make certain that they are 
replaced by more efficient ones later. It will help to recog- 



INSTRUCTION IN ARITHMETIC 151 

nize the rate of work as an important "dimension" of the 
ability to do examples. When a pupil is found who does not 
know certain combinations, but is doing the examples by 
an ingenious method of counting, he must be taught these 
combinations. 

An illustration of corrective instruction. A fifth-grade 
class ■ was given the Cleveland Survey Tests 2 to determine 
the types of examples which the pupils could not do with 
standard ability. This information was supplemented by 
oral diagnosis in correcting the defects revealed. The regu- 
lar "class instruction was supplemented at other periods 
in the day by special help to different pupils in the proc- 
esses in which they were weak, and they were required to 
work extra examples in those processes after the help had 
been given. The drill was limited to the four fundamental 
operations with integers and fractions. At the end of a 
month of this kind of instruction, the pupils were given the 
original test a second time. ,, 

In Fig. 27 the record of one pupil, who made some very 
low scores on the first test, is shown. The figure is so drawn 
that if the pupil were just up to standard in each test 
(A, B, C, D, etc.), the fine representing his record would be 
a straight horizontal line. The solid line represents his first 
record and the broken one his second record. Corrective 
work was attempted in Tests A, B, F, I, N, and O, and the 
figure shows a marked improvement was made in these tests. 
By planning the corrective instruction more carefully it is 
probable that a still more uniform development might 
have been obtained. However, as it is we have a striking 
illustration of what can be accomplished when a diag- 

1 Smith, James H., "Individual Variations in Arithmetic"; in Elemen~ 
tary School Journal (November, 1916), vol. 17, p. 198. 

2 These tests are similar to Monroe's Diagnostic Tests except that they 
contain no tests on decimal fractions. 



152 MEASURING THE RESULTS OF TEACHING 

nosis of a pupil is made and the instruction is based upon 
the diagnosis. 

Summary. In this* chapter we have considered the causes 
of and corrections for the following types of class scores; (1) 
below standard in both rate and accuracy; (2) below stand- 




H I J K L U » 

Fig. 27. Showing Two Records op One Pupil on the Cleveland 
Survey Tests. 

First record, solid line. Second record, four weeks later; dotted line, corrective work given 
on Tests A, B, F, I, N, and O. 

ard in rate with satisfactory accuracy; (3) below standard in 
accuracy with satisfactory or high accuracy; (4) scores too 
widely scattered; (5) irregular development. In connection 
with the case of irregular development the value of diagnos- 
tic tests was pointed out. In dealing with individual pupils 
who are below standard analytical diagnosis is helpful for 
discovering the cause of the defect. Several illustrations of 
this method of diagnosis have been given together with the 
correctives for handling each case. 

QUESTIONS AND TOPICS FOR STUDY 

1. Do you think pupils will welcome definite objective standards and 
the use of standardized tests? Why? 

2. If you are using standardized tests make charts showing class (or 
individual) scores in comparison with the standards. Some teachers 



INSTRUCTION IN ARITHMETIC 153 

have found it helpful to have such charts hung in the classroom. 
It is also helpful to bring such charts to the attention of the pa- 
trons of the school* 

3. Make a chart showing how the pupils of your class compare with other 
classes of the same grade and with classes of other grades. 

4. Suppose a pupil is unable to do satisfactorily certain types of exam- 
ples. How would you proceed to locate his particular difficulties? If 
you are teaching arithmetic, try out your plan on some of your pupils. 

5. What device do you use to provide each pupil with the training 
which he needs? What devices are suggested in this chapter? Can 
you suggest additional ones? 

6. Pupils who are excused from drill because they do not need it should 
spend their time doing profitable things. Suggest a number of assign- 
ments which might be made to such pupils. The assignments may 
be in subjects other than arithmetic if it seems wise, but they should 
be such as not to interfere with the instruction of the other pupils. 

7. How do you know that the methods and devices of instruction which 
you are now using are the best? How could you find out? 

8. How do you know that you are not giving too much time to arith- 
metic? How could you find out? 

9. Is a class score which is conspicuously above standard a sign of 
superior teaching? Why? 

10. Construct two tests, each being confined to a single type of example. 
Give both tests to the same pupils jinder the same conditions. Com- 

' pare the two sets of scores. 

11. Scientific experimentation will be necessary to determine the best 
plans of grouping pupils for instruction. These plans are worthy of 
a trial. 

a. In a building place together for drill those pupils which are most 
nearly equal in ability as shown by the tests. 

b. Excuse from drill those who have demonstrated that they are 
above standard. 

c. Have a special "hospital" class for those pupils who have scores 
conspicuously below standard. A pupil's sentence to the "hospi- 
tal" would be until he brought his scores up to standard. 



CHAPTER VI 

THE MEASUREMENT OF ABILITY TO SOLVE PROBLEMS 
AND CORRECTIVE INSTRUCTION 

Description of Monroe's Standardized Reasoning Tests. 
The measurement of the ability of pupils to solve problems 
requires a list of problems whose difficulty or value has been 
determined, because we saw in Chapter I that problems are 
not equally difficult. Monroe's Standardized Reasoning 
Tests consist of a series of three tests: Test I for the fourth 
and fifth grades, Test II for the sixth and seventh grades, 
and Test III for the eighth grade. Two forms of each test 
are available so that when it is desired to test the pupils a 
second or third time, it is not necessary to use the same list 
of problems. Each problem has been given to several hun- 
dred pupils and its value has been determined both for cor- 
rect principle and for correct answer. Thus, each problem 
has two values, one a "principle value," which represents 
the credit to be given for correct reasoning in solving it, 
and the other a "correct answer value," which represents 
the credit given for making the calculations correctly when 
the problem has been worked according to the correct 
principle. 

An important feature of these tests is the manner in which 
the problems were selected. The writer believes that a satis- 
factory reasoning test must be composed of problems which 
are representative in language and content. In order to 
secure such a list the one- and two-step problems in eight 
widely used textbooks, which totaled about nine thousand 
problems, were collected and classified according to the 
language in which they were stated. The necessity for this 



ABILITY TO SOLVE PROBLEMS 155 

classification will be taken up later under the head of 
"Diagnosis." The types of problems used in the tests oc- 
curred in at least five of the eight textbooks, which insures 
that the language of the problems is representative of that 
used by the authors of our textbooks. 

The tests are printed so that the pupil has space to do 
each problem on the test paper beside the printed state- 
ment of it. This eliminates the necessity of copying either 
the problem or the work. Thus, the teacher has a complete 
record of the pupil's work which is valuable for making an 
analytical diagnosis. The following problems will illustrate 
the nature of the tests : 

A farmer raised 500 bushels of wheat Principle value 2 

on a field of 40 acres. What was the Answer value 2 

average yield per acre? 

A tailor uses 9f yds. of cloth for a suit. Principle value 1 

How many yards will it take for 32 Answer value 2 

suits? 

A field is 20 rods long, and 12 rods wide. Principle value 2 

How many rods of fence are needed Answer value 1 

to enclose it? 

How much more is earned per day by a Principle value 3 

man receiving $30 per week than by Answer value 2 

a man earning $18 per week? 

Method of giving the tests. Detailed instructions for giv- 
ing the tests are printed on the test sheets and thus need 
not be repeated here. One point, perhaps, should be ex- 
plained. In the case of silent reading and the operations of 
arithmetic, we have emphasized the fact that ability was 
"two-dimensional"; that is, that the rate was important as 
well as the comprehension or accuracy. In solving a prob- 
lem, the relative importance of rate as a "dimension" of the 
ability is less, but probably should not be neglected. Ac- 



156 MEASURING THE RESULTS OF TEACHING 

cordingly the directions for giving the tests require the pupil 
to mark the problem which he is working on at the end of a 
given number of minutes and then he is allowed to finish 
the test. This gives a rate score and also a score independent 
of the rate of work. 

Scoring the test papers. Instructions for scoring the pa- 
pers are furnished with the tests, but certain points should 
be noted here. In order that the "ability to reason" may 
be measured separately from the "ability to perform opera- 
tions," each problem is marked for both "correct principle" 
and "correct answer." A solution is marked correct in 
principle when it shows that the pupil has reasoned cor- 
rectly. If a pupil fails to remember correctly some fact, 
such as the number of pounds in a bushel of wheat or the 
number of square feet in a square yard, his reasoning is not 
affected. An answer is counted as correct when (1) the solu- 
tion is correct in principle and (2) also the answer is numer- 
ically correct and in its lowest terms. 

Each pupil is given three scores: (1) "Rate of reasoning," 
which is the sum of the "principle values" of the problems 
solved within the time limit allowed. (2) " Correct reason- 
ing," which is the sum of the "principle values" of all the 
problems solved correctly in principle. (3) "Correct an- 
swer," which is the sum of the "correct answer values" 
of those problems which were solved correctly in principle 
and for which the correct answer was obtained. 

Recording the scores. The class record sheet is similar to 
that used for Monroe's Standardized Silent Reading Tests. 
A blank for recording the third score is provided. This 
record sheet and detailed instructions for recording the 
scores are furnished with the tests. The median scores of 
the class may be calculated either by the directions given 
for the Standardized Silent Reading Tests on page 29, or 
by the directions for Series B on page 104. 



ABILITY TO SOLVE PROBLEMS 157 

Standards. These tests have been used only in a prelim- 
inary form, and for this reason standards have not yet been 
announced. However, standards will be determined as soon 
as reports have been received from a sufficient number of 
schools, and any one who is interested may obtain them by 
writing the Bureau of Cooperative Research, Indiana Uni- 
versity, Bloomington, Indiana. 

Interpretation of class records. Because the final form of 
these reasoning tests has not been used, it is not possible to 
give typical class records upon which to base this discussion 
of the interpretation of scores. However, the preliminary 
form was given to over thirteen thousand pupils, and upon 
the basis of these results types of situations which require 
correction can be predicted with a high degree of certainty : 
Type I, low median score for "Rate of reasoning"; Type II, 
low median score in "correct reasoning"; Type III, low me- 
dian score in "correct answer" indicating inaccurate calcu- 
lation; Type IV, scores too widely scattered or distributed. 

Type I. Median score for " rate of reasoning " below 
standard. From the nature of the test it is obvious that the 
rate of reasoning is not measured separately from the rate of 
calculation, for a pupil not only "reasons out" a problem, 
but also performs the necessary operations before he pro- 
ceeds to the next one. Hence, the "rate of reasoning" score 
is a measure of the rate of reasoning plus the rate of calcula- 
tion. For this reason a score may be below standard either 
because the pupil was slow in his reasoning or because he 
was slow in performing the operations. This fact must be 
kept in mind in interpreting this type. 

In the preliminary test some classes worked much more 
slowly than others, apparently because they had not formed 
the habit of working rapidly. This was probably due to the 
teacher failing to recognize the rate of work as important. 
The writer doe's not believe the rate of work is as important 



158 MEASURING THE RESULTS OF TEACHING 

in solving problems as in performing the operations of arith- 
metic, but it is his judgment that the rate of reasoning should 
not be neglected. The teacher should at least occasionally 
time pupils when they are solving problems, telling them, 
however, that it is more important to have their work right 
than to solve a large number of problems. 

Stone l tells of the case of one pupil who had not learned 
how to work rapidly : 

Pupil, H. C. 

Diagnosis: Up to standard in reading ability, did not indulge 
in undue labeling, physical examination showed no defects, con- 
stantly made low scores. Conclusion as to cause of low score: 
Mental laziness with lack of realization of the passing of time. 

Treatment: The pupil was first of all made conscious of his 
status by comparing his score with those of his fellow classmates 
and with the standard; then he was helped to study his way of 
working which convinced him of the seat of his difficulty. From 
day to day lists of approximately equivalent problems were given 
him with time limit. Much was made of record of scores, gain 
being expected by both teacher and pupil. 

Results: Within a few days notable gain appeared, due to in- 
creased ability to direct and hold attention to the work in hand. 
Contrasted with his previous tendency to wander, the pupil be- 
came capable of working continuously in spite of such distractions 
as people entering the room. After about twenty minutes daily 
for three weeks he raised his score from 4 to 5.4. 2 Though this is 
not a large gain in score, the boy had made it largely of his own 
initiative; he had formed an ideal of concentration, and the con- 
cept of giving attention to reasoning processes was well under way. 
It is believed by those who have studied the boy that much of his 
improvement was due to the convincingness of the objective evi- 
dence of his need to improve. 

Some pupils worked slowly because apparently they did 
not know how to think out the plan of solution. They would 

1 Stone, C. W., Standardized Reasoning Tests in Arithmetic and How to 
Utilize Them. Teachers College (1916), p. 23. 

2 These scores refer to Stone's Reasoning Tests. 



ABILITY TO SOLVE PROBLEMS 159 

try one plan and then erase their work or cross it out and 
try another plan. In such a case the pupils need to be taught 
how to think. This situation occurs more frequently with 
individual pupils than with whole classes, and for that 
reason the corrective measures will be discussed under that 
head. 

A low median score, due to slowness in performing the 
operations, may occur in two ways. First, the pupils may 
not be trained to perform the operations rapidly. This can 
be verified by giving a test upon the operations such as 
Series B. If their scores on these tests are below standard in 
rate, the correctives given on page 123 should be applied. 
Second, the pupils may be recording their work in some 
particular form which the teacher requires. The pupils in 
some classes write out the solution in the form of an analysis 
or record in other ways which consume time. Orderliness 
and system are desirable. In a reasonable degree they are 
necessary, especially when the solution of a problem is long. 
But it should always be remembered that they are a means 
or method for making the solution of the problem easier. 
The teacher should not insist upon a particular form or 
system when it interferes with the pupil's work. 

An illustration of low rate of work due to this last cause 
and the effect of corrective treatment is given by Stone: * 

Some pupils of a certain fifth grade 

Diagnosis: Many pupils made very low scores, many papers 
much covered with such statements as, "If one tablet cost 7 cents, 
2 tablets . . . etc." Here was evidently one large source of failure. 

Treatment: Emphasis was placed on the possibility of saving 
time by not writing so much, brief labels were devised, originality 
was encouraged, and approval of pupils and teacher placed on 
briefest adequate statement. 

1 Stone, C. W., Standardized Reasoning Tests in Arithmetic and How to 
Utilize Them. Teachers College (1916), p. 23. 



160 MEASURING THE RESULTS OF TEACHING 

Results : As shown by second test and by daily work, much time 
was saved for reasoning processes. The following parallel columns 
show typical results: 

Pupil, A. K. 

In first test In second test 

They would cost $18. $2.50 X 9 = $22.50 

If one suit cost $2.50, 9 would $2.00 X 9 = $18. 
cost $2.50 X 9 = $22.50. $40.50 

They would cost $40.50. 

Score in first test, 1 l/3. Score in second test, 3. 

Pupil, L. I. C. 

In first test In second test 

If he sold 4 papers and got twenty 5 One half would be 10 
cents for them, one half would be 10 4_ cents and he could buy 
cents, and with the other 10 cents he 20 ^ ve * 
bought Sunday papers, he would buy 
as many as 2 will go into 10 or 

2 )10 Score in second test, 4 l/2. 

5 papers. 
Score in first test, 3. 

Type II. Below standard in correct reasoning. In order 
to understand the reasons for a class being below standard 
in reasoning and the corrective measures which should be 
used, it is necessary to understand just what is required of 
the pupil in solving a problem. The process of solving a 
problem by reflective thinking may be described in the 
following steps: 

1. It is necessary that the pupil read the statement of the 
problem with understanding. This is a complex process and 
involves several abilities: eye-movement, perception, asso- 
ciation of meaning with symbols, and combining the several 
elements of meaning into an understanding of the problem. 
Out of this should come a definition of the problem, which 



ABILITY TO SOLVE PROBLEMS 161 

is the first step in reflective thinking. It should be noted that 
two kinds of words occur in the statement of problems; 
first) words which describe the setting of the problem or the 
particular environment in which it occurs, and second, words 
which define quantities or quantitative relationships. This 
second class of words we may call technical. The meanings 
associated with them must be exact. Take, for example, this 
problem, " What is the value of sugar obtained at a Vermont 
sugar camp if it is worth ten cents per pound and six pounds 
are obtained on an average from each of 1275 maple trees?" 
Words in this problem such as "Vermont," "sugar," 
"maple," and "camp" describe the setting. They have 
nothing to do with the solution of the problem. The tech- 
nical words are such as "value," "per pound," "are ob- 
tained," and "each." They define the relationships which 
exist between the quantities and are cues for formulating 
the hypothesis or plan of solution which is another step in 
the process. 

2. Principles applicable to the problem must be recalled. 
For example, in the problem, "A man invests $893 in some 
property. He sells the property for $1050. What is his rate 
of profit?" it is necessary to recall the principle that the 
rate of profit is calculated upon the amount invested and 
not upon the selling price. The principles and the meanings 
of the technical words are the data or facts which are used 
in the reflective thinking. 

3. The elements of meaning and the recalled principles 
are used in formulating a plan of procedure or hypothesis 
concerning the operations to be performed upon the quanti- 
ties of the problem. In doing this each element of meaning 
must be given its proper weight. A relatively inconspicu- 
ous term may require an operation. For example, in the 
problem, "A rectangular court 72 feet by 120 feet is to be 
paved at a cost of $2 per square yard. What will be the ex- 



162 MEASURING THE RESULTS OF TEACHING 

pense?" the use of "square yard" instead of "square foot" 
in the statement of the problem makes necessary an addi- 
tional operation. 

4. The hypothesis thus formed should be verified. Gen- 
erally this does not occur as an explicit step. It consists of 
seeing that the hypothesis is in agreement with the several 
elements of meaning and the recalled principles. 

5. The operations outlined in the hypothesis are per- 
formed. Strictly speaking, this is not a step in the reasoning 
process. This is completed when a correct plan of action is 
formulated. 

This analysis assumes that the problem is solved by 
reflective thinking. In many cases the pupil does not reflect. 
If it is very familiar he may automatically identify it as 
requiring a particular operation or operations. This may 
happen after only a partial reading of the problem. Under 
any circumstances this procedure is probably more of the 
nature of a "short-circuiting" of the reflecting thinking proc- 
ess than an exception to it. When the problem is unfamiliar 
the pupil may try random guessing at the plan of solution. 

It was noted that the data used in solving a problem come 
from two sources, recalled principles and the meanings of 
the technical words used in the statement. The ability to 
associate the correct meaning with one term does not imply 
the ability to associate the correct meaning with another 
term. The ability to solve the problem, "At §55 each how 
much must a farmer pay for 25 cows? " does not make certain 
the possession of the ability to solve " Find the duty on $600 
worth of clocks at 40% ad valorem," although the same 
operation is required. The technical terms, such as "$55 
each," "pay for," "find the duty," and "ad valorem" are 
sufficiently different so that a pupil might know the mean- 
ing of one set without knowing the meaning of the other. 
The meaning of the technical terms in a problem furnishes 



ABILITY TO SOLVE PROBLEMS 163 

important data or cues for the judgment concerning the 
operations to be performed. In many cases it appears that 
the determining data come from this source. Thus, in meas- 
uring a pupil's ability to solve printed problems we are meas- 
uring his knowledge of technical terms as well as his ability 
to use this knowledge in formulating plans of procedure. 

The reading of problems is difficult because many forms 
of statement are used. The solving of a problem requires a 
careful reading of it with a high degree of understanding 
and such reading of problems is a more complex and difficult 
task than we commonly realize. Problems are stated in 
many forms and the total "technical" vocabulary which is 
required of a pupil by the time he completes the work of the 
elementary school is a large one. For an illustration, take 
this problem situation: Given $7.50 paid for silk and price 
per yard $1.50, to find number of yards purchased. Exclud- 
ing different arrangements of the words used, twenty-eight 
different forms of statement were found in examining eight 
textbooks for describing this problem situation, and addi- 
tional forms could be constructed. 

1. How many yards of silk at $1.50 per yard can be bought for 
$7.50? 

2. The silk for a dress cost $7.50. How many yards were pur- 
chased at $1.50 per yard? 

3. At $1.50 per yard, how many yards of silk does a woman get 
if the amount of the purchase is $7.50? 

4. At the rate of $1.50 per yard my bill for silk was $7.50. How 
many yards were purchased? 

5. How many yards of silk at $1.50 a yard does a bill of $7.50 
represent? 

6. When silk is $1.50 a yard, a piece of silk costs $7.50. How 
many yards in the piece? 

7. At $1.50 a yard how many yards of silk does a merchant sell 
if he receives $7.50 for the piece? 

8. Mrs. Jones purchased silk at $1.50 a yard. The entire amount 
paid was $7.50. How many yards were bought? 



164 MEASURING THE RESULTS OF TEACHING 

9. Silk was sold at $1.50 per yard. A check for $7.50 was given 
in settlement. Find the number of yards bought. 

10. At $1.50 per yard, how many yards can be bought for $7.50? 

11. A merchant sells a number of yards of silk for $7.50. The 
price being $1.50 for each yard, how many does he sell? 

12. I invested $7.50 in silk at $1.50 per yard. How many yards 
did I buy? 

13. When silk is $1.50 per yard, how many yards can be bought 
for $7.50? 

14. When silk is sold for $1.50 for each yard, what quantity can 
be bought for $7.50? 

15. At the rate of $1.50 per yard, how many yards can be bought 
for $7.50? 

16. Silk is selling for $1.50 per yard, how many yards should be 
sold for $7.50? 

17. At a cost of $1.50 a yard, how many yards can be bought for 
$7.50? 

18. Silk was bought at a cost of $1.50 per yard. At that rate, 
how many yards can be bought for $7.50? 

19. At $1.50 a yard a piece of silk cost $7.50. How many yards 
in the piece? 

20. How many yards of silk at $1.50 can I buy for $7.50? 

21. $7.50 was paid for silk at $1.50 per yard. How many yards 
were bought? 

22. Find the number of yards; cost $7.50. Price per yard $1.50. 

23. The cost of a piece of cloth is $7.50 and the cost per yard is 
$1.50. How many yards are there in the piece? 

24. A woman paid $7.50 for a piece of silk that cost her $1.50 per 
yard. How many yards were there in the piece? 

25. A woman had $7.50 and bought silk at $1.50 a yard. How 
many yards did she buy? 

26. A quantity of silk at $1.50 per yard cost $7.50. What was the 
quantity? 

27. Silk is $1.50 a yard and I bought $7.50 worth to-day. How 
many yards did I buy? 

28. A woman's bill for silk was $7.50. If each yard cost $1.50, 
how many yards were bought? 

This illustration of the variety of terms which are used in 
the statement of one problem becomes more significant 



ABILITY TO SOLVE PROBLEMS 



1C5 



when we remember that this is just one problem and a rela- 
tively simple one. It should be clear that learning to read 
problems is not an easy matter. 

A test to measure a pupil's knowledge of words used in 
problems. The test given below was devised to measure a 
pupil's knowledge of the meaning of words used in stating 
problems. The words in this test were found to be "com- 
mon" to three or four of the newer textbooks for the grades 
in which the test was given. A preliminary test was given 
first to insure that the pupils would understand what the 
test asked them to do. 



Name. 



Vocabulary Test in Arithmetic l 
Grade 



1. Put w beside each word that tells what a man's work is. 

2. Put m beside each word about money. 

S. Put I beside each word that might be used about land. 
4. Put i beside each word that is the name of something to put 
things in. 



basin 


area 


merchant 


profit 


salary 


carpenter 


cashier 


pasture 


retail 


field 


building lot 


earn 


mason 


bin 


attend 


collect 


basket 


real estate 


teamster 


tank 


lot 


poultry 


jars 


acre 


bucket 


fares 


debts 


income 


rent 


dealer 


gardener 


insurance 


machinist 


tailor 


expenses 


miller 


coins 


barrel 


nickel 


cistern 


broker 


wages 


owe 


customer 


excavate 


commission 


schedule 





In Table XVIII the per cent of pupils in both the fourth 
and fifth grades who failed to mark the words correctly is 
given. Thus, forty per cent of fourth-grade pupils and 

1 Chase, Sara E, "Waste in Arithmetic," Teachers College Record 
(September, 1917), vol. 18, p. 364. 



166 MEASURING THE RESULTS OF TEACHING 



Table XVIH. Showing Per Cent of Failures on Vocabu- 
lary Test in Arithmetic 



Grade 


IV 


V 


26% 


20% 


40 


20 


SO 


16 


78 


36 


13 


8 


9 


12 


30 


16 


56 


28 


35 


28 


26 


16 


56 


45 


4 


4 


91 


36 


26 


8 


9 


8 


43 


20 


100 


68 


40 


36 


65 


60 


35 


28 


13 


4 


30 


32 


70 


28 


100 


68 



Grade 



IV 



salary 

retail 

mason 

basket 

lot 

bucket 

rent 

machinist. . 

coins 

broker 

excavate... 

area 

carpenter . . 

field 

bin 

real estate . 

poultry 

fares 

dealer 

tailor 

barrel 

wages 

commission 



merchant . . 
cashier .... 
building lot 

attend 

teamster... 

jars 

debts 

gardener. . . 
expenses . . . 

nickel 

owe 

schedule. . . 

profit 

pasture 

earn 

collect 

tank 

acre 

income .... 
insurance . . 

miller 

cistern .... 
customer. . 



45% 
52 
65 
4 
88 
40 
91 
17 
65 
13 
91 
17 
78 
52 
60 
17 
65 
56 
96 
91 
26 
100 . 
35 



24% 

20 

32 

4 
40 
16 
32 

8 
20 
16 
60 

4 
45 
32 
36 

8 
36 
32 
41 
42 
12 
88 
44 



twenty per cent of fifth-grade pupils failed to mark "sal- 
ary" as a "word about money." All of the words in this 
list are not technical terms, but a number, such as "salary," 
"rent," "area," "field," and "bin," are used in designating 
the relationship of quantities in problems. For example, 
"A man receives $185 per month. What is his yearly sal- 
ary?" or, "A house rents for $40 per month. How much is 
that a year?" In the first problem a pupil cannot reason 
about the situation unless he knows that "salary" refers to 
the "$185 per month" which the man receives. 



ABILITY TO SOLVE PROBLEMS 



1C7 



In another test pupils were asked to draw the figures 
named in Table XIX. The numbers in the table are the 
per cent of pupils in each grade who failed to draw the cor- 
rect figure. 



Table XIX. Showing Per Cent of Pupils who failed to draw 

CORRECTLY THE FIGURES NAMED 



Square 

Rectangle 

Triangle 

Oblong 

Rectangular plot 



III 



10 

100 

50 

15 



Grades 



IV 



4 
89 
35 
40 
87 



8 
80 
20 

4 
68 



These two simple tests show something of what the situ- 
ation in arithmetic probably is. We are asking pupils to 
solve problems when they do not know the meaning of the 
terms used in the problems. We must, therefore, begin to 
give explicit instruction in the meaning of technical terms. 

When a class is below standard in correct reasoning, one 
of two conditions exists. First is a case of ignorance; the 
pupils do not know the meaning of the technical terms or 
cannot recall the required principles and facts. The second 
may be the lack of knowing how to use this information or 
the lack of a sufficient motive. After examining the test 
papers of several thousand pupils, it is the writer's judg- 
ment that the first is the more frequent condition, but often 
pupils fail to reason correctly in solving problems because 
they have no plan of thinking. We saw in the case of silent 
reading that one cause of poor comprehension was the fail- 



168 MEASURING THE RESULTS OF TEACHING 

ure to verify the meaning obtained. In solving problems 
pupils "accept" an incorrect solution because they do not 
verify their plan; that is, they omit the fourth step in the 
process as outlined on page 162. 

The general correctives are suggested by the above analy- 
sis. The pupils should be taught the arithmetical meaning 
of the technical terms used in stating problems. They 
should also be trained to have a good procedure, to be 
somewhat systematic in their reasoning. Especially should 
emphasis be placed upon the step of verification. 

Type in. Below standard in calculation. These tests 
were not designed to measure ability to perform the opera- 
tions of arithmetic. For this reason too much importance 
should not be attached to the "correct answer" scores; but 
when these scores show a class to be conspicuously below 
standard in calculation, the pupils should be given one of 
the series of tests described in Chapter IV. If these tests 
show the class to be below standard, the correctives pre- 
scribed in Chapter V should be used. Only one point needs 
comment here. If a class is found to be up to or above stand- 
ard when tested on the operations separately, then the 
teacher has the problem of causing the pupils to use this 
ability in solving problems. Then the teacher should give 
less "isolated" drill — that is, drill upon examples — and 
more practice in the solving of problems. 

A frequent source of error is the copying of figures. Some 
pupils copy the wrong figures, as 85 for 55. Others write all 
numbers as dollars pointing off two places. Still others, 
when they wish to subtract 240 from 60000, write 

60000 
240 



Type IV. Scores widely scattered. As in silent reading 
and the operations of arithmetic, frequently the scores of a 



ABILITY TO SOLVE PROBLEMS 169 

class will be found widely scattered or distributed. Some 
pupils will have relatively high scores, others will have very 
low scores. The remedy is to give individual or group in- 
struction to those who have low scores. Those who have 
high scores also need special instruction. It may be that 
they should devote some of the time which they are now 
giving to the problems of arithmetic to some other subject. 
A few cases may be adjusted by a reclassification. The cor- 
rective instruction for those below standard can be best 
presented in connection with certain typical errors. 

Neglect of certain technical words. An examination of 
ninety-five fourth-grade test papers revealed the following 
solutions of this problem: "How much more is earned per 
day by a man receiving $30 per week than by a man re- 
ceiving $18 per week?" 

Solutions correct in principle 23 pupils 

30 + 18=48 15 " 

30 - 18 = 12 38 " 

30 X 18 = 540 4 " 

30 - 18 = 22 2 " 

30 - 18 = 28 2 " 

30 X 18 = 130 2 " 

$3.00 and $5.00 3 " 

30 - 18 = 12/30 more 2 " 

3018 4- 7=4148 1 " 

30 + 10 = 40 1 " 

30 X 18 = 60.6 1 " 

The solutions "30 - 18 = 12," "30 - 18 - 22," and 
"30 — 18 = 28" indicate that the pupils neglected the 
technical phrase "per day." If this phrase did not occur in 
the problem these solutions would be correct in principle. 
It might be that some of the pupils did not know the sig- 
nificance of this term. Solutions such as "30 + 18 = 48" 
and "30 X 18 = 540" indicate either a complete ignorance 



170 MEASURING THE RESULTS OF TEACHING 

of the technical term, "how much more," or failure to 
reason at all. 

In the case of this problem, "A car contains 72,060 lbs. of 
wheat. How much is it worth at 87 cents a bushel? " many 
fifth-grade pupils gave no evidence that the number of 
pounds must be reduced to bushels. In the problem, " What 
are the average daily earnings of a boy who receives $0.88, 
$0.25, $1.15, $0.75, $0.50, and $0.60 in one week ?" a very 
large per cent of the pupils failed to pay attention to the 
word "average." Its presence in the problem requires that 
the sum of the earnings be divided by 6. 

The corrective for the neglect of technical terms is to 
teach the pupils their meanings. In this case the pupils who 
simply subtracted 18 from 30 need to be taught that "how 
much per day" when the amount is given for the week 
means division by the number of days in the week. When 
pupils do not know the meaning of "average" they must 
be taught. 

Guessing instead of thinking. An excellent illustration of 
this type of procedure is given by Adams. 1 It occurred in an 
English school in what is the equivalent of our seventh 
grade. The problem, "If 7 and 2 make 10, what will 12 and 

6 make? " is not the sort which we are accustomed to, but 
this fact does not destroy the value of the illustration: 

A look of dismay passed over the seventy-odd faces as this ap- 
parently meaningless question was read. Everybody knew that 

7 and 2 did n't make 10, so that was nonsense. But even if it had 
been sense, what was the use of it? For everybody knew that 12 
and 6 make 18 — nobody needed the help of 7 and 2 to find that 
out. Nobody knew exactly how to treat this strange problem. 

Fat John Thomson, from the foot of the class, raised his hand, 
and when asked what he wanted, said: — 
"Please, sir, what rule is it?" 

1 Adams, John, Exposition and Illustration in Teaching, pp. 176-78. 



ABILITY TO SOLVE PROBLEMS 171 

Mr. Leckie smiled as he answered : — 

"You must find out for yourself, John; what rule do you think 
it is, now?" 

But John had nothing to say to such foolishness. "What's the 
use of giving a fellow a count 1 and not telling him the rule?" — 
that's what John thought. But as it was a heinous sin in Standard 
\T [seventh grade] to have "nothing on your slate," John pro- 
ceeded to put down various figures and dots, and then went on to 
divide and multiply them time about. 

He first multiplied 7 by 2 and got 14. Then, dividing by 10, 
he got 1 2/5. But he did n't like the look of this. He hated frac- 
tions. Besides, he knew from bitter experience that whenever he 
had fractions in his answer he was wrong. 

So he multiplied 14 by 10 this time, and got 140, which certainly 
looked much better, and caused less trouble. 

He thought that 12 ought to come out of 140; they both looked 
nice, easy, good-natured numbers. But when he found that the 
answer was 11 and 8 over, he knew that he had not yet hit upon 
the right tack; for remainders are just as fatal in answers as frac- 
tions. At least, that was John's experience. 

Accordingly, he rubbed out this false move into division, and 
fell back upon multiplication. When he had multiplied 140 by 12, 
he found the answer 1680, which seemed to him a fine, big, sensible 
sort of answer. 

Then he began to wonder whether division was going to work 
this time. As he proceeded to divide by 6, his eyes gleamed with 
triumph. 

"Six into 48, 8 an* no thin' over, — 2 — 8 — an* no remainder. 
I've got it!" 

Here poor John fell back in his seat, folded his arms, and waited 
patiently till his less fortunate fellows had finished. 

James 2 knew from the "if " at the beginning of the question that 
it must be proportion; and since there were five terms, it must be 
compound proportion. That was all plain enough, so he started, 
following his rule: 

"If 7 gives 10, what will 2 give? — less." 
Then he put down 

7: 2:: 10: 

1 Scotch : any kind of arithmetical exercise in school work. • 

2 The clever boy of the class. 



172 MEASURING THE RESULTS OF TEACHING 

"Then if 12 gives 10, what will 6 give? — again less." So he 
put down this time 

12:6 

Then he went on loyally to follow his rule: multiplied all the 
second and third terms together, and duly divided by the product 
of the first two terms. This gave the very unpromising answer 1 3/7. 

He did not at all see how 12 and 6 could make 1 3/7. But that 
was n't his lookout. Let the rule see to that. 

After examining a large number of test papers, this ac- 
count appears to the writer to describe the mental processes 
of a considerable number of pupils. They have not learned 
to think. The teacher insists that they "try" and they put 
down figures. They have been taught that it is worse to 
admit that they cannot solve a problem than to try it 
by unintelligent guessing. It seems that pupils should be 
taught to admit frankly that they do not know something 
when they don't know rather than to try to "bluff." 

The corrective. Pupils are frequently taught to solve by 
rule rather than to reason. Rules are helpful when used 
properly, but teachers should train pupils to think, to as- 
sociate definite meanings with technical terms, to combine 
these meanings and recalled rules into a plan of solution 
and to verify the proposed solution. To do this, the teacher 
should at first use simple problems, such as, "What is the 
area of a field 40 rods by 60 rods?" or, "What is the cost 
of 15 cows at $60 apiece?" and explain to the pupils that 
the words, "What is the area," "WTiat is the cost," to- 
gether with the form of the remainder of the statement of 
the problem, tell one what operation to perform. The words 
used in stating a problem when properly understood tell 
one what the plan of solution should be. Occasionally it is 
necessary to recall rules or principles, but these are sug- 
gested by the words of the problem. If this idea can be 
impressed upon a pupil, progress will have been made in 
teaching him to think. 



ABILITY TO SOLVE PROBLEMS 173 

Illustrations of failure to verify answer. Frequently pu- 
pils give answers which are absurd, thereby furnishing evi- 
dence of failing to apply even a common-sense check to their 
answers. The following are a few illustrations of this practice : 

Problem: "A baker used 3/5 lb. of flour to a loaf of bread. 
How many loaves could he make from a barrel (196 lbs.) of 
flour?" 

Solution: "3/5 of 196 lbs. = 117 3/5 loaves." This solu- 
tion was given by a large number of sixth- and seventh-grade 
pupils. One sixth-grade pupil gave this: "3/5 X 39 =39 1/3 
loaves." 

Problem: " At the rate of $4 for an 8-hour day, how much 
is due a man for 6 1/2 hours work?" 

Solution (sixth grade): "13/2 X 4/1 =$26." This solu- 
tion was given by a considerable number of pupils. Some 
sixth-grade pupils gave this: "8-6 1/2= $2 l/2." One 
gave this, "6 X 4 = 24, 24 X 8 = $272 1/2." 

The corrective. Some teachers recommend requiring pu- 
pils to estimate the answer before beginning the solution. 
For example, in the first problem above, the pupil could de- 
termine whether the number of loaves would be greater or 
less than the number of pounds of flour, 196. In the second 
problem, the pupil could determine whether a man would 
receive more or less for 6 l/2 hours than for 8 hours. This 
makes a common-sense verification a part of the solution 
of a problem. 

Other reasoning tests. Several other tests have been 
devised to measure the abilities of pupils to solve problems 
involving reasoning, but none of them have been widely 
used. Some years ago Stone 1 worked out a reasoning test 

1 Stone, C. W., Arithmetical Abilities and Some Factors Determining 
Them. Teachers College Contributions to Education, no. 19. (1908.) See 
also Stone, C. W., Standardized Reasoning Tests in Arithmetic and How to 
Utilize Them. Teachers College Contributions to Education, no. 83. (1916.) 



174 MEASURING THE RESULTS OF TEACHING 

which has been used in several cities, and in a number of city 
school surveys, so that we have rather definite standards 
as to what may be expected from its use. Starch has devised 
a test which is called Arithmetical Scale A. 1 This scale in- 
cluded a number of the problems used by Stone, Courtis, 
and Thorndike. They have been evaluated upon the basis 
of difficulty and arranged in order of increasing difficulty. 
The pupils are allowed as much time as they need and a 
pupil's score is the value of the most difficult problem done 
correctly. 

QUESTIONS AND TOPICS FOR STUDY 

1. What are the steps in the solving of a problem in arithmetic? 

2. To what extent and how is silent reading involved in solving problems? 

3. Why must the problems which are used in a test be evaluated? 

4. How would you go about teaching a pupil to reason in solving prob- 
lems? 

5. How could you find out whether your pupils are lacking in vocabulary 
or not? 

6. On page 160 why is the form of solution on the second test better than 
the form on the first? 

7. What reasons can you give for the absurd answers and forms of solu- 
tion which many pupils give to problems? How could you correct 
these defects? 

1 Starch, Daniel, "A Scale for Measuring Ability in Arithmetic"; in 
Journal of Educational Psychology, vol. 7, pp. 213-22. 



CHAPTER Vn 

THE MEASUREMENT OF ABILITY IN SPELLING AND 
CORRECTIVE INSTRUCTION 

Making a spelling test. In order that the method of 
measuring ability in spelling may be understood, certain 
things in connection with the making of a spelling test must 
be explained. The following questions are some which must 
be considered: (1) What words should be selected for a test? 
(2) How difficult should the words be? (3) How many words 
should be used? (4) How should they be given? 

(i) Selection of words for a test on the basis of frequency 
of use. The English language contains many words. Some 
of these the average person never uses, others he uses only 
occasionally and a few he uses very frequently. For prac- 
tical purposes there is no advantage in one being able to 
spell words which he never uses, and the makers of courses 
of study and textbooks in spelling are attempting to elim- 
inate these words. Hence, it is obvious that such words 
should not be used to measure the ability of pupils to spell. 
Of the other two classes it is more important to be able to 
spell those words which are used most frequently, and for 
that reason they should be used in a spelling test if it is 
most helpful to the teacher. Hence, the first step in the selec- 
tion of words for a test is to determine what words are used 
most frequently in written language. 

Ayres's determination of the most commonly used words. 
In determining the most commonly used words, the method 
employed has been to examine written material of several 
types, such as letters, newspapers, and children's composi- 
tions, and to obtain a list of the words used and the number 



176 MEASURING THE RESULTS OF TEACHING 

of times each word occurs. Ayres 1 has combined the results 
of four such studies. Two of these studies were based on 
letters, the third upon newspapers, and the fourth upon 
selections of standard literature. The material examined 
in the four studies aggregated 368,000 words, written by 
2500 different persons. 

It was the original intention of Ayres to obtain a list of 
the two thousand most commonly used words, but this was 
impossible because the material examined was found to 
consist of a few words used many times, and of a larger num- 
ber of words used only a very few times. It was found that 
fifty different words were used so frequently that they made 
up approximately half of the material examined. In order 
to secure a list of the thousand most frequently used words, 
it was necessary to include words which were found only 
forty-four times in the 368,000 words of material examined. 
Other studies have been made to determine the words which 
are used most frequently in written language, but the re- 
sulting lists have not been arranged in a form which is con- 
venient to use for testing purposes. Hence, we shall limit 
this discussion of the measurement of spelling ability to the 
one thousand words of Ayres 's list which is published with 
the title A Measuring Scale for Ability in Spelling. 2 How- 
ever, one other study may be mentioned to illustrate further 
this method of determining the words which should receive 
attention in teaching spelling and in the measurement of 
spelling ability. 

Jones's list of words used by school-children. Jones 
collected compositions from pupils in Grades two to eight 
inclusive. In order that a record of the complete writing 

1 Ayres, L. P., Measurement of Ability in Spelling. Bulletin of the Divi- 
sion of Education, Russell Sage Foundation. (New York City, 1915.) 

2 The reader should have a copy of this scale in order to properly under- 
stand this chapter. See Appendix for directions for ordering a sample 
package of tests. 



ABILITY IN SPELLING 177 

vocabulary of each pupil might be obtained, a large number 
of compositions were written, the number per pupil ranging 
from 56 to 105. A total of 75,000 themes, consisting of a total 
of 15,000,000 words and written by 1050 pupils residing in 
four States, were examined. However, only 4532 different 
words were used by these pupils. Unfortunately, Jones does 
not tell us how many times each word was used so that we 
cannot obtain a list of the words which the children used 
most frequently. 

(2) Determination of the difficulty of words. After we 
have a list of the most commonly used words, such as Ayres 
has given us, there remains the problem of determining the 
relative difficulty of the several words. It is a well-known 
fact that some words are more difficult to spell than others. 1 
The words included in a test either must be equal in diffi- 
culty or their relative difficulties must be known. Otherwise 
we will be using a measuring instrument consisting of un- 
equal units, but will be considering the units to be equal. 
Doing this makes our measurements inaccurate. The spell- 
ing difficulty of words for a given group of children may be 
determined by having the words spelled by them. From 
the per cent of correct spellings of each word the relative 
difficulty of the words may be calculated. Words which are 
misspelled an equal per cent of times by pupils of a given 
grade are equal in difficulty for that group. In the absence 
of this information it is practically impossible for a teacher 
to judge the difficulty of the words. Buckingham concluded 
that the judgment of a single teacher is almost of no value. 
"It may be good and it may be bad; and it is about as 
likely to be the one as the other." 

1 The spelling difficulty of a word has two interpretations. It may be 
taken to mean the difficulty which children have in learning to spell it. 
It may also refer to the frequency with which it is misspelled. The latter 
meaning will be used in this chapter. 



178 MEASURING THE RESULTS OF TEACHING 

How Ayres determined the difficulty of the words in his 
list. To determine the words of equal difficulty and the rela- 
tive difficulty of the groups of words, Ayres divided the 
thousand words into fifty lists of twenty words each. Each 
list of words was spelled by the children of two consecutive 
grades in a number of cities. The thousand words were 
then divided into another fifty lists of twenty words each. 
Each of the new lists was spelled by the children in four 
consecutive grades. In all, 70,000 children spelled twenty 
words, making a total of 1,400,000 spellings, or an average of 
fourteen hundred spellings of each of the thousand words. 

Upon the basis of this information Ayres classified the 
words into twenty-six groups, the words of each group being 
approximately equally difficult for school-children of a 
given grade. 1 This classified list, together with the per cent 
of pupils in each of the grades who spelled the words of each 
list correctly, has been printed with the title, Measuring 
Scale for Ability in Spelling. Strictly speaking, the Ayres 
Measuring Scale for Ability in Spelling is not a measuring 
instrument in itself, but rather a list of the foundation words 
of the English language, classified into twenty-six groups 
according to spelling difficulty. The teacher may use this 
list as a source of words for constructing spelling tests. 

Pupils are not tested when words are too easy. When a 
pupil spells correctly all of the words of a given list, we do 
not have a measure of his spelling ability. We simply 
know that he can spell these words correctly; we do not have 
any information concerning how far beyond this list his 
spelling ability extends. In fact, the pupil has been given no 
opportunity to show how well he can spell. It is a well- 
known fact that the pupils of any grade or of any class are 
not equal in ability, but exhibit a wide range of ability. 

1 For the details of the method employed see Ayres, L. P., Measurement 
of Spelling Ability, pp. 22-35. 



ABILITY IN SPELLING 



179 



Thus, in testing a class it is necessary to use words for which 
the average per cent of correct spellings is less than one hun- 
dred. Ayres recommends that in making a test for the 



Number of 
pupils 

15 



10 



II 




10 



15 



20 



Number of 
words ^ 
spelled correctly 

Fig. 28. Showing the Distribution op 91 Pupils according to the 
Number of Words spelled correctly. 

Class average, 84 per cent. 

pupils of a given grade, the words be taken from the column 
for which an average of eighty-four per cent of correct 
spellings may be expected. 1 

Fig. 28 represents a typical result of using the words 
chosen as Ayres recommends. Compare the shape of this 
distribution with the shape of Figs. 1 and 2. These fig- 

1 The reader should not confuse scores or measures of ability with school 
marks. The per cent of correct spellings is a measure. The school mark is 
the meaning which the school attaches to that measure. The fact that both 
the measure and the school mark may be expressed in per cents does not 
make them the same. 



180 MEASURING THE RESULTS OF TEACHING 

ures were presented as evidence that teachers' marks were 
inaccurate. The class average is eighty-four per cent, but 
those pupils who spelled all of the words correctly have not 
been tested. Those who misspelled only one or two words 
probably have not been tested satisfactorily. 

Otis 1 presents facts from which he concludes that the most 
reliable measures of spelling ability are obtained by using 
words for which there is an average of fifty per cent of cor- 
rect spellings. In support of this conclusion he points out 
that a list of words for which the average per cent of correct 
spellings was either zero per cent or one hundred per cent, 
would yield a measure of zero reliability. Likewise a list of 
words for which the average per cent of correct spellings 
was ten per cent or ninety per cent, would yield measures 
only slightly more reliable. Hence, it seems natural that 
the most reliable measures would be obtained by using a 
list for which the average per cent of correct spellings was 
fifty. On the other hand, some writers claim that it is not 
wise to have pupils spell words incorrectly. They point out 
that every repetition tends to fix a habit. 

Ayres gives no satisfactory justification for recommend- 
ing the choice of words for which an average of eighty-four 
per cent of correct spellings may be expected. When meas- 
uring the spelling ability of children in Springfield, Illinois, 
Ayres used words for which seventy per cent of correct 
spellings had been obtained. For the Survey of Cleveland, 
Ohio, the words were chosen from columns for which the 
average per cent of correct spellings was seventy-three. 
Thorndike has used words for which the per cent of cor- 
rect spelling is fifty. 2 For these reasons it is probably best 

1 Otis, A. S., "The Reliability of Spelling Scales"; in School and So- 
ciety, vol. 4, p. 753. 

2 Thorndike, E. L., "Means of Measuring School Achievement in Spell- 
ing"; in Educational Administration and Supervision, vol. 1, p. 306. 



ABILITY IN SPELLING 181 

to choose words from columns for which the average per 
cent of correct spellings is approximately seventy. 

(3) How many words to use. Another question which 
must be considered in making a spelling test is the number 
of words it is necessary to use. In general the ability to spell 
one word is separate and distinct from the ability to spell 
any other word. Ability to spell, therefore, consists of a large 
number of abilities to spell specific words. This being the 
case it would be necessary to use all of the thousand words 
of Ayres's list in order to obtain a complete and accurate 
measure of a pupil's ability to spell the most commonly 
used words. However, it is possible to secure a measure 
which is representative of the pupil's ability to spell these 
words by using a smaller number of words. This is possible 
in just the same way that it is possible to determine the 
quality of a load of wheat or a vat of cream by the examina- 
tion of a sample. 

How many words are necessary in making a spelling test 
depends upon what is desired. Relying upon the theory of 
random sampling, Thorndike believes a small number of 
words is sufficient to measure the spelling achievement of a 
large school system. A test consisting of only ten words has 
been used in a number of school surveys. This number is 
probably sufficient for the measure of a large school system, 
but if it is desired to obtain a measure of the spelling ability 
of individual pupils, a larger number must be used. Otis l 
says that a twenty-five-word test gives a very poor measure 
of individual ability, and that at least one hundred words 
should be used, better four hundred or five hundred words. 
Starch recommends the use of two hundred words. There- 
fore, it is probably best to use as large a list of words as the 
time which the teacher can use for measuring spelling will 
permit. At least fifty words should be used if possible. 
1 hoc. cit., pp. 679, 682. 



182 MEASURING THE RESULTS OF TEACHING 

(4) How should the words be given. The complaint is 
frequently made that pupils spell words correctly in the 
spelling class, but misspell the same words when writing 
compositions and other school exercises. One reason why 
this occurs is that in the spelling class the pupil has his atten- 
tion fixed upon the spelling of the word and takes time to do 
his best. In writing a composition, his attention must be 
centered upon what he is writing, and thus he is able to give 
only partial attention to the spelling. Also he probably 
writes more rapidly. Hence, we may recognize two types of 
spelling ability: (1) the ability to spell words when one's 
attention is focused upon the spelling; (2) the ability to 
spell words when one's attention is focused upon other things 
and the spelling is carried on in the margin of consciousness. 

The words which make up a test may be dictated to the 
pupils as separate words, or they may be embedded in sen- 
tences which are dictated. Furthermore, the dictation of the 
sentences may be timed so that the pupils are forced to write 
at their normal rate. In this way we are able to secure ap- 
proximately the second type of spelling. Investigation has 
shown that the per cent of correct spellings is higher when 
the words are dictated separately than when they are dic- 
tated in timed sentences and the pupils are forced to write 
at their normal rate. According to Courtis the per cent of 
correct spellings is about five greater when the words are 
dictated in lists. Fordyce has found this difference to be 
between ten and fifteen per cent. The writer has found a 
difference of more than six per cent. 

In writing letters, compositions, and the like, the spelling 
must be carried on in the margin of the attention because 
the ideas which are being expressed must occupy the focus 
of the attention. This is particularly true of the foundation 
words of the language such as we have in the Ayres list. 
The words of this list constitute over ninety per cent of the 



ABILITY IN SPELLING 183 

words we use. Hence, by using the words embedded in sen- 
tences and dictated rapidly enough to force the child to 
write at his normal rate, we measure the spelling ability 
which functions in one's every-day writing. 

The rate of dictation. Pupils may be caused to write at 
approximately their normal rate by dictating the sentences 
at that rate. The Freeman's standards for rate of handwrit- 
ing are as follows in terms of letters per minute: second 
grade, 36 letters; third grade, 48 letters; fourth grade, 56 
letters; fifth grade, 65 letters; sixth grade, 72 letters; sev- 
enth grade, 80 letters; eighth grade, 90 letters. The dicta- 
tion of a sentence requires some additional time, probably 
ten per cent. For example, in the case of the sixth grade, 
instead of dictating at the rate of 72 letters in one minute, 
66 seconds should be allowed for words totaling 72 letters. 
On this basis the number of seconds to be allowed per letter 
for the several grades are as follows: — 

Grade Seconds per letter 

n 1.83 

in 1.38 

IV 1.18 

V 1.01 

VI 92 

VEI 83 

vm 73 

If the sentences contain more than thirty to forty letters, 
they should be dictated in sections, so that the pupil's writ- 
ing will not be slowed up by trying to recall what has been 
dictated. Furthermore, tests of rate in handwriting have 
shown that all pupils do not normally write at the same rate. 
For this reason provision must be made for those pupils 
who are accustomed to write more slowly than the standard 
rate. This can be done by having none of the test words 
come at the end of the sentences, and requiring all pupils to 



184 MEASURING THE RESULTS OF TEACHING 

begin upon the next sentence as soon as it is dictated, even 
if they have not finished writing the preceding. 

Summary : The discussion of the making of a spelling test 
may be summarized as follows: 

1. The Ayres Measuring Scale for Ability in Spelling is 
a list of the one thousand most commonly used words of the 
English language. These words have been classified accord- 
ing to difficulty and words chosen from one column may be 
considered as being equally difficult. When words are taken 
from more than one column the inequality of difficulty must 
be recognized, if an accurate measure is to be secured. 

2. Twenty words are probably sufficient to secure a reli- 
able measure of the spelling ability of a class. At least fifty 
words should be used to secure a reliable measure of the 
spelling ability of individual pupils. More accurate meas- 
ures will be obtained by using one hundred words. In the 
case of the upper grades it will be necessary to use words 
from more than one column. When this is done the relative 
difficulty of the words must be recognized to secure an accu- 
rate measure. 

3. In order that the words may be difficult enough to 
really measure the spelling ability of all pupils, the' words 
should be chosen from columns for which the standard per 
cent of correct spellings is approximately seventy. For the 
lower grades it is probably best to use words for which the 
standard per cent of correct spellings is from fifty to sixty- 
six. If the words are to be used in timed sentences it will 
probably be satisfactory to use easier words. 

4. In order to secure the best measurement of spelling 
ability, the words should be embedded in sentences, and the 
sentences dictated at approximately the standard rate of 
handwriting for the grade. Test words should not occur at 
the end of the sentences. 

A timed sentence spelling test. In order to illustrate the 



ABILITY IN SPELLING 185 

type of test described above, we reproduce the directions 
and a test arranged for the fourth grade. The rate of dicta- 
tion of this test was determined upon the basis of measure- 
ments of the handwriting rate of six thousand Kansas 
school-children. 

Directions for Giving a Timed-Sentence Test 

1. See that the pupils are provided with two or three sheets of 
paper and with either pencil or pen and ink. If pencils are to be 
used they should be well sharpened. If pen and ink are used, 
good pens should be provided. 

2. Make certain that all pupils understand what they are to 
do. It is well to give a short preliminary practice in writing from 
dictation if the pupils are not accustomed to it. For this purpose 
use some simple selection. 

3. It is well not to tell the pupils that they are being tested in 
spelling. Under no circumstances indicate the test words by 
emphasis in dictating. 

4. When everything is ready, say to the pupils: "I have some 
sentences which I want you to write as I dictate them. I am 
going to dictate them rather rapidly, possibly more rapidly than 
some of you can write. If you have not finished writing one sen- 
tence when I begin to dictate another, I want you to leave it and 
begin on the new sentence. If there are any words you cannot 
spell, you may omit them. Take time to dot your i's and cross volu- 
te. If you have any question about what you are to do, ask it 
now, because you cannot ask questions after I begin to dictate.'* 

5. Use the arrangement of the sentences which has been pre- 
pared for the grade you are testing. If a teacher has two divisions 
of different grades, as 5B and 6A, she must test the two divisions 
separately, using the test which is arranged for each grade. When 
the second hand of your watch is at 60 read the first sentence. 
When the second hand reaches the next number printed in the 
margin, read the second sentence. Dictate the other sentences 
at the time indicated. Dictate the sentences distinctly, but do 
not repeat. Be careful not to suggest the spelling of the words by 
unduly emphasizing certain syllables. It is advisable for the 
teacher to practice dictating the sentences according to the direc- 
tions before attempting it with a class. 



186 MEASURING THE RESULTS OF TEACHING 

6. Stop the pupils promptly at the time indicated. Allow no 
corrections or additions to be made. Ask the pupils to turn their 
papers over and write their name and grade. Appoint two or 
three pupils to collect the papers. 

A Timed-Sentence Test arranged for the Fourth Grade 

Test words taken from column M of the Ayres Scale 
Seconds 

60 He bought a railroad ticket to the city. 
41 Collect the account before Sunday. 

18 Those children will return soon. 
53 Anyway she is ready to go. 

19 Please omit both names. 
44 Few change trains here. 

9 He says the great office is full. 
43 Who died this morning? 

6 The money for the picture was paid to us. 
47 The members did not understand him. 

24 Again he took the car. 

46 It will provide an income in his old age. 
27 The army had begun to drill in the park. 

7 He might begin the contract next week. 

47 I was unable to recover the bill. 
21 I have an errfra dress with me. 
51 The deal was almost closed. 

19 Did you inform him to follow the car? 
56 The past month I was in the south. 
30 While he goes home, you stay. 
58 The car was driven beside the train. 
35 I saw him enter the place. 

When the second hand reaches 1, stop the writing. 

Allow no corrections or additions to be made. Ask the pupils to 
turn their papers over and write their name and grade. Appoint 
two or three pupils to collect the papers. 

Marking the test papers. The most accurate results will 
be obtained when the teacher marks the test papers for 
incorrect spellings and omissions of test words, but unless 



ABILITY IN SPELLING 187 

the teacher has sufficient time for this work the papers may 
be marked by the pupils. When this plan is followed the 
teacher should spell out the test words and have the pupils 
mark with a cross words misspelled and words omitted. 
(When a timed-sentence test is used no attention is given 
to words which are not test words.) The number of test 
words correctly spelled should be written at the top of each 
pupil's paper. This is the pupil's score. By dividing the 
number of words spelled correctly by the number in the 
test, the per cent correct is obtained. 

Recording the scores. For recording the scores of a class 
a record sheet such as shown in Fig. 29 should be used. 
(This record sheet is used for a fifty-word test.) In this way 
the teacher obtains a statement of the number of pupils who 
spelled forty words correctly, the number who spelled forty- 
one words correctly, etc. The class score may be found by 
adding the scores of all of the pupils together and dividing 
this sum by the number of pupils. This quotient is the aver- 
age. For practical purposes it is just as satisfactory and 
more convenient to find the median. This may be done by 
arranging the test papers in the order of the number of 
words spelled correctly, the lowest score on the bottom. 
The score on the middle paper is the median score. 

Standards : (1) The Ayres Scale. In classifying the words 
of his list according to difficulty, Ayres determined the 
average per cent of the pupils of each grade who spelled the 
words correctly. Thus the words of column O were spelled 
correctly by 50 per cent of the third-grade pupils, 73 per 
cent of the fourth-grade pupils, 84 per cent of the fifth-grade 
pupils, 92 per cent of the sixth-grade pupils, 96 per cent of 
the seventh-grade pupils, and 99 per cent of the eighth- 
grade pupils. These per cents, which are printed at the head 
of each column, represent the average spelling ability of 
pupils in the several grades when the words are dictated in 



188 MEASURING THE RESULTS OF TEACHING 

Distribution of Pupils' Scores 



Number of words 
spelled correctly 


Number of pupils 


Number of words 
spelled correctly 


Number of pupils 


50 




Sub. Total 




49 




24 




43 




23 




47 




22 




46 




21 




46 




20 




44 




19 




43 




18 




42 




17 












40 




15 












38 




13 












36 




11 












34 




9 












32 




7 












30 




5 












28 




3 












'26 




1 












Sub- Total 




Total 













Fig. 29. Showing the Record Sheet for recording Pupils' Scores 
on a Spelling Test of Fifty Words 



ABILITY IN SPELLING 189 

lists. When the words are used in timed sentences the aver- 
ages have been 5 to 15 per cent lower. 

It may be seriously questioned whether the averages 
which Ayres gives are satisfactory standards of spelling 
ability for the foundation words of the language. Ayres 
says: "Probably the scale will have served its greatest use- 
fulness in any locality when the school-children have mas- 
tered these one thousand words so thoroughly that the scale 
has become quite useless as a measuring instrument." In 
the past we have not had the advantage of such a list and 
have distributed our efforts in teaching spelling over a very 
much larger list of words. If we accept these one thousand 
words as the foundation words of our language, we should 
place prime emphasis upon teaching them.' This being the 
case a satisfactory eighth-grade standard would approxi- 
mate one hundred per cent for all of the words. For the pre- 
ceding grades the standard would be one hundred per cent 
for the words of the list which the pupils had been taught. 
For example, the easiest nine hundred words might be used 
for the seventh grade, the easiest seven hundred and fifty 
for the sixth grade, and so forth. The use of the scale in the 
way Ayres suggests would seem to lead to standards of this 
type. The distribution of the words among the several 
grades and the optimum standards must be determined by 
experimentation. 

(2) Timed-sentence spelling tests. A series of timed-sen- 
tence spelling tests similar to the one reproduced on page 
186 was given to several thousand children in Kansas about 
the seventh month of the school year. The median scores 
are given in Table XX, and they may be used as tentative 
standards for timed-sentence spelling tests of the type re- 
produced on page 186, but it must be remembered that as 
we improve our teaching of spelling our standards should be 
raised. 



190 MEASURING THE RESULTS OF TEACHING 

Table XX. Showing Median Scores for a Timed-Sentence 
Spelling Test of Fifty Words 



Grade 


Number of 
pupils tested 


Median scores. 

Number of 

words spelled 

correctly 


Per cent of 

words spelled 

correctly 


Ayres's stand- 
ards 


III 


997 
1060 
1009 
870 
826 
608 


28 
39 
33 
40 
35 
42 


56 
78 
66 
80 
70 
84 


66 


IV 


84 


V 


73 


VI 


84 


VII 


79* 


VIII 


88* 







* The test for the seventh and eighth grades consisted of words taken from three col- 
umns. Hence these standards are only approximate. 

Causes of low class scores. As in the case of other sub- 
jects the teacher should use the results of spelling tests as a 
basis for planning instruction which will correct the defects 
that the tests reveal. A class score below standard indi- 
cates an unsatisfactory condition which may be due to one 
or more of the following conditions : 

1. The class as a whole may be unable to spell certain 
words. 

2. Certain pupils may be unable to spell a large number 
of the words of the test. 

3. The errors may be rather uniformly distributed as to 
both words and pupils. 

To determine the extent to which each condition causes 
the low class average, the teacher should make the follow- 
ing type of tabulation from the test papers. This will 
give a record of each pupil for each word of the test. In- 
stead of designating the pupil by number as in this illustra- 
tion their names or initials can be used at the head of the 
columns. 



ABILITY IN SPELLING 



191 



Words of the test 


Pupils 


1 

c 
c 
c 
c 
c 
c 


o 

c 
c 
c 

c 


3 

c 
c 
c 
c 
c 


4 

c 
c 
c 

c 


5 
c 

c 
c 

c 


6 

c 

c 
c 
c 
c 


7 

c 
c 
c 

c 


8 

c 
c 
c 

c 


9 
c 



c 
c 
c 


10 

c 
c 
c 
c 
c 
c 


11 

c 


12 














unless 


c 











c indicates the word was correctly spelled. 



Although these words are listed by Ayres in his Spelling 
Scale as being equally difficult for pupils in general, they 
are not necessarily so for particular pupils. Obviously in 
the class here represented "catch" and "clothing" need 
general emphasis, while only certain pupils need to give 
attention to "black," "began," and "unless." Pupil 11 has 
misspelled five out of six words, and hence probably is a 
"poor speller." 

What a spelling test reveals. Such a tabulation of the 
results of a test is valuable because it reveals the character 
of the spelling ability of the class. It points out the "poor 
spellers." It indicates whether the class as a whole find some 
words difficult to spell or the misspellings are uniformly dis- 
tributed. However, it must be remembered that the test 
contains only a limited number of words, and although the 
results may be accepted as indicating the nature of the con- 
ditions which exist, it cannot tell the teacher all the words 
for which corrective instruction must be planned. Simply 
to know that a pupil is below standard in ability is of little 
value to the teacher, because in general the ability to spell 
one word does not imply ability to spell another word, nor 
does the lack of ability to spell a given word indicate that a 



192 MEASURING THE RESULTS OF TEACHING 

pupil cannot spell another word. But the fact in the above 
illustration that most of the class could not spell correctly 
"catch" and "clothing" indicates that there are several 
words which the class as a whole do not know how to spell. 
On these words class instruction is needed. When the 
teacher knows the type of situation with which he has to 
deal he should then proceed to determine the particular 
words which all or certain pupils need to learn to spell. At 
least the teacher should make a very careful diagnosis of the 
spelling ability of each pupil whose test score is below stand- 
ard, to ascertain just what words he cannot spell of those 
he is expected to spell. 

This is accomplished by giving the pupils below standard 
a test including all of the words which they are expected to 
be able to spell. Such a test is not for the purpose of meas- 
urement, but should be thought of as the first step in the 
teaching of spelling. Each pupil should be required to make 
from this test a list of all the words which he has spelled 
incorrectly. The words of this list are the ones he needs to 
study. It is obvious that to ask a pupil to study words 
which he can already spell correctly is to ask him to use his 
time without profit. 

Class correctives. " Spelling Demons." Certain fre- 
quently used words are very frequently misspelled. Jones 1 
has given us a list of one hundred words which he found 
misspelled most frequently in children's compositions. He 
calls them the " One hundred spelling demons of the English 
language." Nine tenths of these words are found in Jones's 
list for the second and third grades. Four fifths of these words 
are found in Ayres's list. Because these words are frequently 
misspelled and are among the commonly used words of the 
language a teacher will make no mistake in emphasizing 
these words in the teaching of spelling until the pupils can 
spell them correctly. 

1 See pages 176-77 for a description of Jones's study. 



ABILITY IN SPELLING 



193 



The One Hundred Spelling Demons of the English Language 



which 


can't 


guess 


they 


their 


sure 


says 


half 


there 


loose 


having 


break 


separate 


lose 


just 


buy 


don't 


Wednesday 


doctor 


again 


meant 


country 


whether 


very 


business 


February 


believe 


none 


many- 


know 


knew 


week 


friend 


could 


laid 


often 


some 


seems 


tear 


whole 


been 


Tuesday 


choose 


won't 


since 


wear 


tired 


cough 


used 


answer 


grammar 


piece 


always 


two 


minute 


raise 


where 


too 


any 


ache 


women 


ready 


much 


read 


done 


forty 


beginning 


said 


hear 


hour 


blue 


hoarse 


here 


trouble 


though 


shoes 


write 


among 


coming 


to-night 


writing 


busy 


early 


wrote 


heard 


built 


instead 


enough 


does 


color 


easy 


truly 


once 


making 


through 


sugar 


would 


dear 


every 


straight 



Class drill. Courtis 1 recommends a form of class drill 
which may be used when the class as a whole are learn- 
ing to spell a word : 

The word to be learned is pronounced by the teacher and class 
together and then written letter by letter as it is spelled aloud. 
This is repeated five or six times in rapid succession. The rate of 
writing should be slow at first, then faster and faster (like a college 
yell), until at the sixth repetition only the most rapid writers are 
able to keep up with the class. 

Spelling games. In the manual referred to above, Courtis 
describes the following games which may be used for pro- 

1 Courtis, S. A., Teaching Spelling by Plays and Games (82 Eliot Street, 
Detroit, Michigan), p. 8. This is an excellent manual for teachers. It con- 
tains explicit directions for a number of spelling games. 



194 MEASURING THE RESULTS OF TEACHING 

viding drill upon spelling. They are particularly helpful 
when a stronger motive is needed. Each of these games pro- 
vides for dividing the pupils in a room into two teams or 
groups and for keeping scores for a week or a month : 



1. Syllable game. 

2. Jumbled-letter game. 

3. Initial game. 

4. Rhyming game. 

5. Derivative game. 

6. Definition game. 

7. Linked-word game. 

8. Missing-word game. 

9. Composition game. 



Individual correctives. Types of misspellings. A pupil's 
spelling difficulty is not completely diagnosed when the 
words he does not spell correctly are located. Errors in 
spelling are seldom if ever distributed uniformly among the 
several letters composing the word. Neither does it appear 
that there is much uniformity in the location of errors in 
different words. Certain words are misspelled in only a few 
ways, while other words are misspelled in many ways. 
Certain misspellings occur frequently, while others seldom 
occur. In Table XXI the misspellings of certain words found 
in the papers of eighty seventh-grade pupils are given, 
together with the frequency of each. The words were taken 
from column S of the Ayres Scale. Where no number fol- 
lows the word that type of misspelling of the word occurred 
but once. 1 

Causes of some misspellings. A study of Table XXI 
shows that certain forms of misspelling occur more fre- 
quently than others, and that most of the misspellings may 
be attributed to certain specific causes. Forms of misspell- 

1 See also Sears, J. B., Spelling Efficiency in the Oakland Schools. Board 
of Education Bulletin, Oakland, California, p. 51. 



ABILITY IN SPELLING 



195 



Table XXI. The Misspelling of Eighty Seventh-Grade 
Pupils on a Column Spelling Test 



I. affair 


govament 


XIV. particular 


affere 


governement 


particuliar 


affire 


gorvement 


particuler 


afair (2) 


VII. improvement 


partictuler, 


aff aired 


improvment (7) 


pellicular (8) 


affer 


impovement 


particlar 


II. assist 


VHI. investigate 


pertucular 


assit (3) 


investigate (3) 


parte ular 


aisst (2) ' 


envesigatige 


parti ular 


ascist 


investiage 


partular 


assest 


IX. marriage 


paticular 


assaist 


marrage (5) 


perciluar 


asscest 


marage 


pectuliar 


assiast 


merriage 


pecticular 


acsist 


X. mention 


pertictural 


acist (2) 


mension (8) 


patuclure 


accisted 


mensioned 


pecuhar 


assantant 


meantion (2) 


peetulair 


assised 


menchion 


XV. possible 


accessese 


XI. motion 


possable (4) 


accest 


moshen 


posible 


astist 


moticem 


posable 


assis 


motation 


posiable (2) 


assite 


montion 


possiable (5) 


HI. certain 


XII. neither 


posobile 


certian (7) 


neather (6) 


possibbe 


serten 


nether 


posiple 


sertain 


niether (2) 


XVI. serious 


certin 


nieghter 


cyreaua 


secrtain 


XIII. opinion 


cerrious 


IV. difference 


oppinion (5) 


scerious 


differance (10) 


opinon (2) 


serrious (2) 


diffierence 


opinton 


cerious 


V. examination 


oppoinen 


sereaus 


examation (10) 


oppinum 


XVH. stopped 


examition 


oppenion (2) 


stoped (13) 


examnition 


opion (3) 


stopts 


excamation 


oponion (2) 


stocted 


excanitions 


oppion (2) 


stop 


examanation (.3) 


opinnion 




VI. government 


opoin (2) 




goverment (9) 


opionion 





ing such as " partiular," "partuler," "opinon," "impove- 
ment," "possibbe," are probably due to carelessness or ac- 
cident, " a slip of the pen." Relatively few of the misspell- 
ings in this table may be assigned to this cause. Errors of 
this type probably cannot be entirely eliminated from un- 



196 MEASURING THE RESULTS OF TEACHING 

corrected manuscript. However, drill will reduce the num- 
ber of such errors to a satisfactory minimum. 1 

An important source of error is mispronunciation of the 
word by the pupil. He may have acquired this from the 
teacher, but more likely from those with whom he associates 
outside of school. Or it may have been acquired from lack 
of attention to the form of the word. Such misspellings as 
the following are probably caused by mispronunciation: 
"perticular," "particlar," "investagate," "goverment," 
"examation." 

A very striking instance of this type of spelling error and 
its cause came to the attention of the writer a few years ago. 
A man who had taught geometry for a number of years 
used the word "frustum" in a manuscript, spelling it "frus- 
trum" which agreed with his pronunciation of the word. 
This manuscript was read by a number of well-known 
mathematicians who read it critically. Only two noted the 
misspelling of the word, and one mathematician, who took 
much pride in his ability to spell correctly and who was the 
author of several textbooks, admitted that he had always 
pronounced and spelled the word "frustrum." 

Other errors listed in Table XXI are due to certain phonic 
irregularities of the English language, for example, certain 
misspellings of "assist," "certain," "affair," "marriage," 
"motion," "neither," and "serious." Such errors occur 
more frequently in connection with vowels than with con- 
sonants. Still other errors, such as "stoped," and "improve- 
ment," are due to certain doubled or silent letters. 

The length of words and the position of the letters are 
responsible for some errors. In general there is a close agree- 
ment between the number of letters in a word and its rela- 

1 Errors of this type have been called "lapses." 'See Hollingworth, 
Leta S., The Psychology of Special Disability in Spelling, Teachers College, 
Columbia University, Contributions to Education, no. 88, p. 38, for a com- 
plete statement of types. 



ABILITY IN SPELLING 197 

tive difficulty. The longer the word, the more difficult it is 
to spell. In Table XXI it is obvious that the errors are not 
uniformly distributed among the several letters of a word. 
For example, consider " examination/ ' the fifth word in the 
table. The letters e-x and t-i-o-n were given correctly in 
every case. The first a also occurs. In every case except 
one, the letter m is given. Fifteen out of the seventeen 
errors occur in connection with three letters, i-n-a. The 
explanation of this condition, which is typical, is that correct 
spelling "depends mainly upon a correct visual or audile 
image coordinated with the correct motor control." l 
Some letters are more conspicuous than others in the form 
of the printed, or written, word and also in the sound of 
the spoken word. In general, the letters occupying the 
initial positions are remembered best for this reason. 

Some words are spelled incorrectly because the pupil has 
not learned any spelling, correct or incorrect, for the word. 
In such cases if the pupil is asked to spell the same word 
several times, different spellings will be given. Holling- 
worth gives an illustration of this type. One pupil mis- 
spelled "saucer" in seven different ways in nine successive 
writings of the word: "s-a-u-e-c," "s-u-s-s-e," "s-u-c-c-e-r," 
"s-u-c-c-e-r-e," "s-u-r-r-e-s," "s-u-s-s-e-r," "s-u-c-e," 
"s-u-s-s-e-r," "s-u-c-c-e-r." Other words are misspelled 
because the pupil has learned an incorrect spelling. This 
was the case in the misspelling of "frustum" described 
above. 

Still another cause of misspelling is a lack of the knowledge 
of the meaning of the word. Hollingworth states: 2 

On the basis of these data we conclude that knowledge of meaning 
is probably in and of itself an important determinant of error in 

1 Kallom, Arthur W., "Some Causes of Misspellings"; in Journal of 
Educational Psychology, vol. 8, p. 395. 

2 Psychology of Special Disability in Spelling, p. 57. 



198 MEASURING THE RESULTS OF TEACHING 

spelling; that children will produce about sixty-six and two-thirds 
per cent more of misspellings in writing words of the meanings of 
which they are ignorant or uncertain, than they will produce in writing 
words the meaning of which they know. 

Teaching the pupil to correct his errors in spelling. 
Spelling consists in forming correct and fixed associations 
" between the successive letters of a word and between the 
word thus spelled and the meaning." l The laws governing 
the formation of fixed associations are those of habit forma- 
tion. The first step in habit formation is to get the atten- 
tion of the child focused upon the associations to be formed. 
The second step is to secure sufficient repetition. Repetition 
of the associations is secured both through drill and through 
using the word in written expression. The pupil must give 
attention to the repetitions of the associations in order to 
insure that wrong associations will not be made. 

The causes of misspelling given above suggest certain 
correctives. If the error is due to an incorrect pronuncia- 
tion of the word, the pupil should be taught the correct 
pronunciation. The phonic irregularities of words should 
be emphasized. In the case of long words the pupil's atten- 
tion should be directed to the letters in the middle of the 
word. The meaning of the word should be connected with 
the pupil's experience. This does not mean merely requiring 
him to use it in a sentence. 

As in the case of other school subjects motive is an im- 
portant faotor in learning to spell. A strong motive can be 
secured by the use of standardized spelling tests. Definite 
standards should be set and at intervals careful tests should 
be made. Charts showing the scores of the individual pupils 
as well as the class score in comparison with the standard 
will be helpful. 

1 Freeman, F. N., Psyclwlogy of the Common Branches, p. 115. 



ABILITY IN SPELLING 199 

Numerous experiments have shown that pupils can spell 
correctly a large per cent of the words in the lists in spellers 
before they have studied them. Because of this fact the 
assignment of the spelling lesson should include the dicta- 
tion of the words to the pupils so that each might know what 
words he needed to study. The teacher would also learn 
what words he should emphasize in his instruction. 

Some writers state that a pupil should not be permitted 
to spell a word incorrectly when it can be avoided, and for 
this reason pupils should learn to spell words correctly be- 
fore they are required to write them. Just how important 
it is to do this we do not know. In certain cases it appears 
that a child or an adult learns to spell certain words cor- 
rectly by having his attention directed to his errors. The 
fact of his error serves to direct his attention to learning to 
spell the word correctly. Those who believe that evil effects 
will come from having pupils write words which they cannot 
spell correctly, may direct them to omit those words which 
they think they cannot spell correctly. 

The dictation of the words in assigning the spelling lesson, 
together with the detailed testing of the pupils as suggested 
on page 191, reveals to the teacher the words upon which 
he must exercise his ability as a teacher of spelling. It also 
reveals to him the pupils to whom instruction should be 
directed in the case of each word. Particular methods and 
devices by means of which the laws of habit formation may 
be fulfilled are described in books which deal with the 
teaching of spelling. 1 

A device for focusing attention upon the difficult portion 
of a word. In teaching the spelling of a word the child's 
attention should be directed to the crucial associations. 
If the word is one like "government," his attention should 

1 A very good chapter (vi) will be found in Freeman's Psychology of the 
Common Branches. See also Cook and O'Shea, The Child and his Spelling. 



200 MEASURING THE RESULTS OF TEACHING 

be called to the correct pronunciation. If it is such a word 
as "their," his attention should be called to the use of the 
word. To eliminate spelling errors a pupil's attention 
should be called to his particular error and he should be 
helped to remove the cause. If the cause is mispronuncia- 
tion, see that he learns to pronounce the word correctly. If 
the error is due to a confusion of letters, the pupil should be 
given some device to prevent this confusion. The following 
is a device which may be used for especially difficult words : 

Par-tic-u-lar 

I frequently misspell in writing compositions but now 

I am going to learn to spell it correctly. My teacher tells me that 

I do not look at the syllables and letters closely enough. 

I am going to do it now with care. I see that the word 

has syllables. The first syllable is The vowel 

of this syllable is , the first letter of the alphabet. The 

last syllable is and the vowel is also The 

word contains letters, the other vowels are 

and Now that I have looked at the word carefully I 

am going to be very in spelling it. I am also going to be 

in pronouncing it. I am going to remember that the 

vowel in the first syllable and in the last syllable is an 

I am not going to pronounce those syllables as if the vowel were e 

instead of I am going to be very about both 

spelling and pronouncing this word. I want it to be correct in 
every 

This device is used by providing the pupil who needs 
instruction with a printed or typewritten copy. The pupil 
is required to fill in the blank spaces correctly. This is re- 
peated until the correct associations are fixed. 

Drill for making associations automatic. Getting the 
pupil to spell a word correctly is only the first step. There 
must be attentive repetitions of the correct associations 
until they have become automatic. In this respect spelling 
is similar to arithmetic. In the teaching of the operations 



ABILITY IN SPELLING 201 

of arithmetic, drill occupies a prominent place, but in the 
case of spelling our teaching has been confined primarily to 
testing pupils. Requiring pupils to write each misspelled 
word ten or twenty times is an effort to provide practice. 
Such practice is unsatisfactory. After the first writing of the 
word the pupil probably copies. Hence the repetitions are 
not attentive. 

Practice upon words which are misspelled by a majority 
of the pupils can be secured by having them recur in the 
spelling lesson from day to day. This plan provides the 
same drill for all pupils regardless of whether they misspell 
the word or not. In this respect it is unsatisfactory. The 
pupils may be required to write material which the teacher 
dictates. When carrying on this kind of practice, the 
teacher dictates as rapidly as the pupils can write, or better, 
calculates the number of seconds required to write each sen- 
tence, or part of sentence, as was done for the timed-sen- 
tence spelling test. (See page 186.) This can easily be done 
by using the rates given on page 183. 

" Developing a spelling consciousness." The following 
device serves to direct the pupil to see his errors in a whole- 
some way. It has yielded very gratifying results in the 
Training School of the Kansas State Normal: 1 

When the spelling sentences or lists have been written, 
each pupil is required (1) to mark each word, the spelling 
of which he doubts; (2) as far as possible he is encouraged 
to test the validity of his doubts by known means outside 
of the dictionary, finally checking up all doubted words by 
using the dictionary; and (3) he then writes all of the mis- 
spelled words, which he has thus detected, correctly spelled 
in separate lists; (4) at this point the pupils' papers are ex- 
changed, the teacher spelling all words and the pupils 

1 Lull, Herbert G., "A Plan for Developing a Spelling Consciousness"; 
in Elementary School Journal, vol. 17, p. 355. 



202 MEASURING THE RESULTS OF TEACHING 

marking those found to be misspelled on the papers; and 
finally (5), when the papers are returned to their owners 
the additional misspelled words discovered should be added 
to their individual lists. 

The pupil's spelling is scored by the teacher on the basis 
of the correctness of his doubts as well as upon the number 
of words spelled correctly. In the absence of a scientific 
determination of the relative significance of spelling of words 
correctly and doubting correctly, the same value is assigned to 
each. The pupils are scored both for doubting words spelled 
correctly, and for not doubting words spelled incorrectly. 

QUESTIONS AND TOPICS FOR STUDY 

1. Measure the spelling ability of the pupils of your class by means of a 
timed-sentence test and then dictate the test words as separate words. 
Compare the two sets of scores. 

2. Teachers frequently tell with pride that all but two or three of their 
pupils make a "grade of 100" on a certain test. Should the fact be a 
cause for a feeling of satisfaction? Were the pupils really tested? 

3. Dictate the words for the next spelling lesson before the pupils have 
studied them. Have each pupil make a list of the words which he 
misspells and also of the particular misspellings which he has used. 
Direct the pupils to base their study upon these lists. 

4. Construct a series of "timed-sentence spelling tests" for the elemen- 
tary school, using suitable words from the Ayres Scale. 

5. Why does a test of easy words fail to give a measure of spelling 
ability? 

6. Why must the relative difficulty of the words of a test be known if 
accurate measures are desired? 

7. Make a study of the ways in which your pupils misspell words. Also 
ascertain the causes for these misspellings. 

8. How can you use this information in making your teaching of spelling 
more effective? 



CHAPTER VIII 

THE MEASUREMENT OF ABILITY IN HANDWRITING 

The measurement of ability in handwriting involves 
(1) the measurement of the rate of writing and (2) the qual- 
ity. The rate is measured by having the pupil write under 
specified conditions for a convenient number of minutes and 
counting the number of letters written per minute. The 
measurement of quality is accomplished by securing a 
sample of the pupil's handwriting and determining the speci- 
men on a handwriting scale which is equivalent to it in 
quality. The quality may also be measured by means of 
a score card. 

The measurement of the rate of handwriting. In measur- 
ing the rate of handwriting certain points must be kept in 
mind. 

(1) The teacher should see that all pupils are provided 
with good pen-points, ink, and paper unless they use pen- 
cils, in which case there should be a sufficient supply of well- 
sharpened pencils. All pupils should be supplied with two 
or three sheets of suitable writing-paper. 

(2) The pupils should be asked to write a sentence or a 
paragraph which they have memorized. To guard against 
lapses of memory, the pupils should be asked to repeat in 
concert the selection to be used. If convenient it is well to 
provide each pupil with a printed or typewritten copy of 
the selection. When this cannot be done, the selection may 
be written on the blackboard where all can see it. The 
selection should contain no words which the pupils cannot 
spell readily. It is well to have them practice writing the 
more difficult words before the test is begun. Do not use 
material which the pupils must compose as they write, for 



204 MEASURING THE RESULTS OF TEACHING 

this would be worthless in testing. The rate of writing un- 
familiar material from a printed copy will vary with the 
pupil's rate of reading and so will not give a true measure 
of his rate. Dictated material should be used only when 
the teacher wishes to control the rate, not when the rate 
is to be measured. 

(3) The teacher must be provided with a watch which 
has a second-hand or with a stop-watch. A two- or three- 
minute period should be allowed and the teacher should 
exercise care to make this period exact. 

(4) Pupils probably have two or more rates of writing, 
one for the penmanship class when they are doing their best 
and another for writing exercises in history, language, or 
other school subjects. The way in which the teacher gives 
the directions to the class will influence their rate. If he 
tells the pupils or even suggests that they are expected to 
show how well they can write, the rate will probably be 
low. On the other hand, if the pupils are given the idea 
that the rate is most important, they will write more rapidly 
than they are accustomed to do. It is, therefore, important 
that a teacher follow directions which have been prepared 
for securing samples of pupils' handwriting. We give below 
a set of directions which have been widely used. 

Directions for Obtaining Samples 

"When children have paper and pencil proceed thus : Read aloud 
a stanza — four lines of the poem, "Mary had a little lamb," etc., 
which is printed below. If you are using these directions for the 
first time use the first stanza; if the second time, use the second 
stanza; if the third time, use the third stanza. Have the children 
recite this stanza aloud in unison until you are sure they all know 
it. Then ask them to write it once. Collect these copies and destroy 
them. Do not tell the children they are to be tested in any way. Next 
instruct the children as follows: 

"Write the stanza of the poem which you have learned. Write 
it just as you would in a composition or in an ordinary school 



ABILITY IN HANDWRITING 205 

exercise. If you finish the stanza, write it over again, and keep 
on writing until I tell you to stop. Write on only one side of the 
paper. W T hen you fill one page use another. We must start to- 
gether and stop together. Lay your papers on your desk in posi- 
tion. Have pen and ink ready. WTien I say 'Get ready,' ink your 
pen and place your hand in position to write, but do not begin to 
write until I say 'Start.' Then all begin at once. When I say 
'Stop' I want you all to stop at once and raise your hands so that I 
can see that you have stopped." 

Now take your watch in hand and when the second-hand reaches 
the 55 second mark say, "Get ready." Exactly at the 60 second 
mark say, "Start." At the end of three minutes call out, "Stop, 
hands up." Be sure to allow exactly three minutes. Have each 
child write name and age on the back of the paper. Collect the sam- 
ples at once and put them together. 

I 

5 10 15 

Mary had a little lamb, 

20 25 30 35 40 

Its fleece was white as snow; 

45 50 55 60 65 

And everywhere that Mary went 

70 75 80 84 

The lamb was sure to go. 

n 

5 10 15 20 25 

He followed her to school one day; 

30 35 40 45 

That was against the rule; 

50 55 60 65 70 75 

It made the children laugh and play 

80 85 90 95 97 

To see the lamb in school. 

m 

5 10 15 20 25 

And so the teacher turned him out, 

30 35 40 45 

But still he lingered near, 

50 55 60 65 70 

And waited patiently about 

75 80 85 89 

Till Mary did appear. 



206 MEASURING THE RESULTS OF TEACHING 

Directions for securing samples for the " Gettysburg 
Edition " of the Ayres Scale. With the "Gettysburg Edi- 
tion" of his handwriting scale Ayres gives directions which 
should be followed when that scale is used. The directions 
are not entirely complete and should be supplemented by 
the last two paragraphs of the directions given above. 

To secure samples of handwriting the teacher should write on 
the board the first three sentences of Lincoln's Gettysburg Address 
and have the pupils read and copy until familiar with it. They 
should then copy it, beginning at a given signal and writing for 
precisely two minutes. They should write in ink on ruled paper. 
The copy with the count of the letters is as follows: 

Four 4 score 9 and 12 seven 17 years 22 ago 25 our 28 fathers 
35 brought 42 forth 47 upon 51 this 55 continent 64 a 65 new 68 
nation 74 conceived 83 in 85 liberty 92 and 95 dedicated 104 to 106 
the 109 proposition 120 that 124 all 127 men 130 are 133 created 
140 equal 145. Now 148 we 150 are 153 engaged 160 in 162 a 163 
great 168 civil 173 war 176 testing 183 whether 190 that 194 nation 
200 or 202 any 205 nation 211 so 213 conceived 222 and 225 so 227 
dedicated 236 can 239 long 243 endure 249. We 251 are 254 met 
257 on 259 a 260 great 265 battlefield 276 of 278 that 282 war 285. 

Other selections which have been used. Different inves- 
tigators have required pupils to write different material. 
Several have used the first line or the first stanza of the poem 
"Mary had a little lamb," which is reproduced above. " Sing 
a song of sixpence" has been used. Other sentences which 
have furnished copy are: "Jolly kings bring gifts while 
happy maids dance." "A quick brown fox jumps over the 
lazy dog." ! "Then the carelessly dressed gentleman stepped 
lightly into Warren's carriage and held out a small card. 
John vanished behind the bushes and the carriage moved 
along down the driveway." 2 

1 This sentence was used in securing specimens for the Freeman Scale. 
It contains all of the letters of the alphabet. 

2 These sentences were used in securing the specimens for the Thorndike 
Scale. 



ABILITY IN HANDWRITING 207 

In the Cleveland Survey the first three sentences of Lin- 
coln's Gettysburg Address were written, and Ayres has used 
this selection in the "Gettysburg Edition" of his scale. In 
several school surveys the pupils were allowed to write any 
familiar stanza of a poem. The chief principles to bear in 
mind in selecting materials are: (1) to use material in the 
lower grades which will not furnish difficulties in spelling 
and remembering; and (2) to use material which will be 
uniform in all classes which are to be compared. 

Marking the papers for rate of handwriting. Time can be 
saved by making use of the numbered selections given above. 
Divide the total number of letters written by the number 
of minutes allowed. The quotient is the number of letters 
per minute. This is the pupil's rate score and should be 
written in the upper right-hand corner of his paper. 

Measuring the quality of handwriting by means of scales. 
The "quality" of a sample of handwriting may be measured 
by means of a "handwriting scale" which consists of a 
number of specimens of handwriting arranged in order of 
"quality." The process of measurement simply consists of 
moving the sample which is being measured along the scale 
until a specimen of the scale is found which "matches " it in 
"quality." The process is much like "matching" a sample of 
dress material or ribbon. Skill in this "matching" or use of 
the scale comes with practice and it is recommended that a 
teacher prepare himself by at least a short period of training. 

Handwriting scales. The scales in most general use are 
the ones constructed by Thorndike 1 and by Ayres. 2 

1 Thorndike, E. L., " Handwriting "; in Teachers College Record (March, 
1910), vol. 2, no. 5. The scale may be purchased from the Bureau of 
Publications, Teachers College, Columbia University, New York City. 

2 Ayres, L. P., A Scale for Measuring the Handwriting of School-Children. 
(Russell Sage Foundation, Bulletin 113.) Ayres has also constructed an 
adult scale.and the " Gettysburg Edition." In this book the term " Ayres's 
Scale" refers to the "Gettysburg Edition" unless otherwise noted. 



208 MEASURING THE RESULTS OF TEACHING 

Thorndike constructed his scale on the basis of three 
characteristics — beauty, legibility, and general merit. The 
degree of these characteristics represented in the specimens 
of the scale was determined by the consensus of opinion of 
competent judges. Ayres constructed his scale on the basis 
of legibility alone. He defined legibility in terms of ease of 
reading. That specimen was defined as most legible which 
was read most easily. The numerical values of the speci- 
mens of the Thorndike Scale range from 4 to 18, one or more 
specimens being given for each degree of quality. 

Ayres's Scale, "Three-Slant Edition," consists of three 
types of specimens, vertical, semi-slant, and full slant. Each 
of these three types is represented by eight degrees of qual- 
ity to which are assigned the numerical values 20, 30, 40, 
up to 90. In using this scale it must be remembered that 
these values are not the same as the per cents used in 
reporting "grades." 

Ayres 1 later devised a scale from specimens of hand- 
writing written by adults. Trained judges used the "Three- 
Slant Edition" in selecting the specimens and in deter- 
mining their values. This "Adult Scale" is similar to the 
"Three-Slant Edition" in its general plan. Very recently 
(1917) Ayres devised a third scale, the "Gettysburg Edi- 
tion." This scale differs from the others in the following 
particulars: It has one specimen for each step. The speci- 
mens are written on ruled paper. The copy is the same for 
all specimens. In addition to the specimens of the scale, 
this edition has directions for securing specimens from a 
class and for scoring these specimens. It also furnishes stand- 
ards for rate and quality of handwriting for the grades above 
the fourth. Ayres asserts that the purpose of these changes 
is "to increase the reliability of measurements of hand- 

1 Ayres, L. P., A Scale for Measuring the Handwriting of Adults. (Russell 
Sage Foundation, Bulletin E 138.) 



ABILITY IN HANDWRITING 209 

writing." A recent investigation 1 shows that measurements 
made by this scale are more reliable than when made by 
the "Three-Slant Edition." 

Following discussion based on the " Gettysburg Edition " 
of Ayres's Scale. Because more reliable measurements may 
be obtained by using the "Gettysburg Edition" of Ayres's 
Scale, we shall base the following discussion upon it. It will, 
however, be an easy matter for any one to adapt it to any 
other scale. In order to understand the following pages the 
teacher should have a copy of this scale. See the Appendix 
for price list and directions for securing a sample package 
of tests. 

Training in the use of a handwriting scale. The accu- 
racy of a teacher's measurements of quality handwriting 
depends upon the method he uses and upon his training in 
the use of that method. When a teacher is using a hand- 
writing scale for the first time the following preliminary 
exercise is recommended : 

Select ten samples at random. Number these samples and place 
their numbers on a blank sheet of paper. Now take the first sample 
and rate it thus: Place the Ayres Scale on a table in full view and 
in a good light. Place the sample directly under the scale division 
marked 20 and move it along toward 90, comparing it with each 
division. Decide which division of the scale it resembles most in 
quality. "Disregard differences in style, but try to find on the scale 
the quality corresponding with that of the sample being scored." 
Then place it under the scale division marked 90 and work back 
toward 20 as before. Decide again which division it resembles 
most in quality. If your two judgments agree, mark the rating 
on the blank paper opposite the numeral 1. If the two judgments 
do not agree, compare the sample again with the two divisions 
of the scale and determine which it most nearly resembles. Proceed 
to rate the other samples in this manner, keeping the record for 

1 Breed, F. S., "The Comparative Accuracy of the Ayres Handwriting 
Scale, Gettysburg Edition"; in Elementary School Journal (February, 1918), 
vol. 18, p. 458. 



210 MEASURING THE RESULTS OF TEACHING 

each. When you have finished the ten samples, lay this record 
aside, out of sight. Rate the ten samples a second time, again 
keeping the records and again laying the records aside. Do this 
a third time, and when you have finished, compare your three rat- 
ings for each of the ten samples. If the three ratings for any one 
sample vary more than ten, satisfy yourself as to which rating is 
the correct one, by comparing it with the scale again. 

When convenient it is better to use samples whose correct 
rating is known. A set of fifty such samples may be obtained 
from the Bureau of Publications, Teachers College, Colum- 
bia University, New York City. They are rated in terms 
of Thorndike's Scale, but these scores can be changed to 
Ayres's Scale by multiplying by 6.7 and subtracting 20 from 
the product. The remainder is the true quality of the 
sample on the Ayres Scale. 

Method of using the scale. For using the "Gettysburg 
Edition" Ayres gives the following directions: 

To score samples slide each specimen along the scale until a 
writing of the same quality is found. The number at the top of the 
scale above this shows the value of the writing being measured. 
Disregard differences in style, but try to find on the scale the quality 
corresponding with that of the sample being scored. With practice 
the scorer will develop the ability to recognize qualities more rap- 
idly and with increasing accuracy. If the scoring is done twice, the 
results will be considerably more accurate than if done only once. 
The procedure may be as follows: Score samples and distribute 
them in piles with all the 20's in one pile, all the 30's in another, 
and so on. Mark these values on the backs of the papers, then 
shuffle the samples and score them a second time. Finally make 
careful decisions to overcome any disagreements in the two scorings. 

Whenever three or more persons can work together in 
scoring specimens the results may be expected to be more 
satisfactory than those secured by independent work. All 
the members of the group should examine the specimen of 
writing and confer concerning the rating it should receive. 



ABILITY IN HANDWRITING 211 

A majority of the group must agree before a score is assigned 
to the specimen. 

A method which will require more time, but one which 
will secure more accurate results than the methods de- 
scribed above, is one in which a group of three or more 
persons score the specimens independently, using the sorting 
method. Then the scores assigned by all of the judges to a 
specimen are averaged and the result taken as the true 
score for that specimen. The accuracy of the resulting scores 
will increase with the size of the group of judges. 

Recording scores. After the samples are rated the teacher 
must be careful that his papers are grouped correctly by 
classes. If he has but one grade of pupils, say fifth grade, 
or two divisions of the same grade, say fifth A and fifth B, 
then his papers may be all grouped together and but one 
distribution made. If, however, he has parts of two or more 
grades, say part fifth and part sixth, he must fill out a sepa- 
rate record sheet for each division. A convenient form of a 
class record sheet is shown in Fig. 30. 

Sort the papers from one class on the basis of quality. 
(For instance, put into one pile all those papers having a 
quality of 90, into another put all the 80's, into another all 
the 70's, and so on.) Then, one pile at a time, re-sort the 
papers in each of these piles on the basis of their score for 
rate, placing together those papers whose rates are 30 to 39, 
40 to 49, 50 to 59, etc. (For example, if there were ten 
papers of quality 60, whose rates were 50, 53, 55, 62, 62, 64, 
69, 72, 77, 80, the first three would be piled together, the 
next four would form a second pile, the next two a third pile, 
and the last one would be placed by itself.) Next count the 
number of papers in each of these piles and record the num- 
bers in the proper vertical column of the table. (In our 
illustration this is the column under 60. There are three 
papers in the pile whose rates are between 50 and 59. Place 



212 MEASURING THE RESULTS OF TEACHING 

a figure 3 in the 60 column and directly opposite the numer- 
als 50 to 59. There are four papers in the pile whose rates 
are 60 to 69. Hence, a figure 4 is to be placed in the 60 col- 
umn and opposite the numerals 60 to 69.) Each of the 
other piles is to be treated in the same way. 

When all the scores have been entered, find the sum of 
the figures in each vertical column and in each horizontal 
row. If your records have been accurately made, the sum 
of the horizontal totals will just equal the sum of the verti- 
cal totals. Save all specimens for future use. 

Computing class scores. The medians of the distributions 
(rate and quality) are used to designate the general standing 
of a class. The method of calculating the median, described 
on page 103, is used. It is necessary to remember that in 
the record sheet shown on page 213, the width of the inter- 
vals is 10, the same as in the accuracy distributions for arith- 
metic. When there are fewer than fifteen pupils in a class 
it is not wise to attach much importance to the medians. 
The distributions and individual scores are more significant. 

Measurement for diagnosis. The quality of a sample of 
handwriting is a complex product. It depends upon several 
characteristics of the handwriting, such as the uniformity 
of slant, uniformity of alignment, letter formation, and 
spacing. There are available two instruments for diagnostic 
measurement: 

1. Freeman's 1 Scale which differs from the other scales in 
an important respect. It is in reality five scales, one for each 
of the following characteristics of handwriting: uniformity 
of slant, uniformity of alignment, quality of line, letter 
formation, and spacing. These five scales are now printed 

1 Freeman, F. N., The Teaching of Eandwriiing. (Houghton Mifflin 
Company, 1915.) Also, "An Analytical Scale for the Judging of Hand- 
writing"; in Elementary School Journal (April, 1915), vol. 15, p. 432. A 
copy of the scale can be obtained from Houghton Mifflin Company, 
Boston. Price 25 cents. 



ABILITY IN HANDWRITING 

Distribution of Pupils' Scores 



213 



Number of letters written 








Quality 








Total 


iji one minute 


20 


30 


40 


60 


60 


70 


80 


90 


for rale 


Below 10 




















10 to 19 




















20 to 29 




















30to 39 




















40 to 49 




















50to 59 




















60 to 69 




















70 to' 79 




















80 to 89 




















90 to 99 




















100 to 109 




















110 to 119 




















120 to 129 




















130 to 139 




















140 to 149 




















Over 150 





























































Approximate Class Medians : Quality. 
True Medians : Quality 



.Rate (Letters per min.). 
.Rate (Letters per min.). 



Fig. 30. Showing Form of 
Scores 



Class Record Sheet for recording 
in Handwriting 



214 MEASURING THE RESULTS OF TEACHING 

on one sheet of paper or chart, and each scale is called a 
division. 

The first of the five divisions of the Freeman Scale repre- 
sents three degrees of uniformity of slant. In using this 
division, as in using the next division, judgments will be 
made more easily if a slant and alignment gauge is used. 1 
The second division represents uniformity of alignment. 
The user must be careful to note that letters which are close 
together show deviations in alignment more prominently 
than letters written farther apart. 

The third division shows the quality of line or stroke. A 
reading-glass will aid in judging with this division. The 
fourth division is intended to measure letter formation. 
Freeman describes eight illegible forms of letters which 
should be counted as errors. Two principles should control 
here: (1) whatever slant or type of script the pupil may use, 
consistency to that choice should be maintained; and (2) no 
letter should vary from its recognized form so much as to 
be easily mistaken for another letter. The fifth division 
shows different kinds of spacing. Letters may be crowded 
or spread too far apart. The same applies to words. 

In each division the three degrees of excellence are given 
scores of 1, 3, and 5 respectively. The intermediate values 
of 2 and 4 may also be used. If the old edition of the scale 
is used, the scores assigned to the specimens of letter forma- 
tion are 2, 6, and 10. Freeman suggests that the specimens 
be scored by using the score for letter formation as placed 
on the new edition of the chart, and then doubling these 
scores in making up the total score. 

1 Freeman, F. N., The Teaching of Handwriting, p. 151. The slant gauge 
consists of three rows of parallel lines. The lines in one row are vertical 
and in each of the other rows the lines are set at a uniform slant. The align- 
ment gauge consists of one straight line four or five inches long. These 
lines may be drawn on transparent paper and placed over a specimen of 
handwriting to assist in determining the deviations from uniformity in 
slant and alignment. 



ABILITY IN HANDWRITING 215 

Using the Freeman Scale. This scale may be used for 
measuring specimens from all members of a class, but fre- 
quently it is used to measure specimens written by those 
ranking conspicuously below the average ability or below 
the standard ability for the class. This needy group of 
pupils may be selected by the teacher's unaided judgment, 
but preferably by the use of the Thorndike or Ayres Scale. 

Freeman * has recently issued the following suggestion for 
using his scale: 

The specimen to be judged is graded according to each category 
separately and given the rank of the specimen in the chart with 
which it most nearly corresponds in each case. The total rank is 
calculated by summing up the five individual ranks. Thus, if 
letter formation is given double value, the lowest possible rank is 
6 and the highest possible rank is 30 (5 + 5 -f 5 + 10 + 5), and 
the range is 24. 

Several precautions are to be observed in making the judgments. 
The value of the method rests upon the fact that different features 
of the writing are singled out, one at a time, and graded by being 
given a rank in one of only three steps. The difference between the 
steps are marked, and the ease of placing a specimen should be 
correspondingly easy. 

This method implies, however, that 

(1) The attention is fixed on only one characteristic at a time. 

(2) The judgment on one point be not allowed to influence the 
judgment on the other point. 

(3) The same fault be counted only once. 

(4) General impressions be disregarded. 

The scores secured by means of the Freeman Scale should 
be saved to furnish a means of evaluating the results secured 
from instruction. The scores may be recorded on the speci- 
men, or, better, on an individual record card, such as shown 
in Fig. 31. The latter will be more convenient when the 

1 Freeman, F. N., Experimental Education, p. 86. (Houghton Mifflin 
Company, 1916.) 



216 MEASURING THE RESULTS OF TEACHING 
Pupil's Name City 





First trial 
Date 


Second trial 
Date 


Third trial 
Dale 


Fourth trial 
Date 


53 ( 


J 


f 


Chart I 
(Slant) 










1 ! 


1 1 
1 


Chart II 
(Alignment) 














Chart III 
(Quality of line) 












Chart IV 
(Letter formation) 










: tt 




Chart V 
(Spacing) 
















Total (value on 
Freeman Scale) 












Quality (value on 
Ayres 8cale) 












Speed 
(Letters per minute) 













Fig. 31. Individual Record Card, Freeman Scale. 

teacher wishes to examine a series of scores recorded at 
intervals over a term of several months. 

2. Grays Score Card for detailed analysis. The score card 
represents another attack upon the problem of measure- 
ment. It requires that the essential elements of handwrit- 
ing be selected and each assigned a value. The score 
card devised by Gray l weights the value of each of the 
essential elements of handwriting so that the highest value 
which can be assigned to slant is 5, while spacing of letters 
may receive 18, neatness, 13, etc. (See Fig. 32.) The use of 
this score card by teachers in their grading of handwriting 
would undoubtedly tend to direct their attention to the 
individual needs of the pupils. So far there is no evidence 
to show that its use will result in more accurate measures 
than the use of any one of the scales. Some claim that 

1 Gray, C. Truman, A Score Card for the Measurement of Handivriting. 
(Bulletin of the University of Texas, no. 37, July, 1915.) j 



ABILITY IN HANDWRITING 

Age Date , 



217 



Pupil 

Grade School 

Sample Number Teacher 



Sample 


Perfect 
score 


Score 


1 


2 


3 


4 


6 


G 


7 


S 


8 


10 


11 


VI 


a 


U 




3 
5 

7 

8 
9 

11 

18 

13 

(26) 
8 
6 
5 
5 
2 




2. Slant 




Uniformity 
Mixed 

3. Size 




Uniformity 
Too large 
Too small 








Uniformity 
Too close 
Too far apart 

6. Spacing of words 
Uniformity 
Too close 
Too far apart 


- 


Uniformity 
Too close 




Blotches 
Carelessness 

































Fig. 32. Standard Score Card for measuring Handwriting. (Devised 
by C. T. Gray.) 

the elements of handwriting have not been correctly evalu- 
ated. However, it has the advantage that its use trains 
the user in the analysis of handwriting. Gray well defends 
the device by saying that agriculturists have long used 



218 MEASURING THE RESULTS OF TEACHING 

such score cards to secure very satisfactory and accurate 
results in judging grain and live-stock. 

In using Gray's Score Card and the Freeman Scale, 
measures of each of the several factors concerned in a 
pupil's handwriting are secured. A record of successive 
measurements will show just what abilities have not been 
sufficiently improved. These abilities will then be the 
points of attack for the teacher and pupil in their subse- 
quent work. For example, a record as shown on the Gray 
Score Card might indicate that a pupil's handwriting was 
suffering chiefly because of poor letter formation. A closer 
inspection would show that letter formation was very 
often defective in two items, letters not closed and parts 
omitted. Such diagnosis reveals a definite problem for the 
teacher. 

Use of the score card. The score card (see page 217) may 
be used for a pupil, or a class. If it is used for a pupil, the 
numerals along the top may be taken to indicate weeks, 
months, or other intervals. In the column under the 
numeral 1 the first scores of a pupil's handwriting should 
be entered. A month later a second series of scores should 
be entered in the column headed by the numeral 2. The 
next month another series of scores should be entered under 
numeral 3, and so on. At the close of a term there will 
appear a very useful record of the child's experience in the 
learning of handwriting. This use of the score card Gray 
calls a clinical study. 

If the card is used for a class, the numerals at the head of 
the columns stand for the specimens written by the several 
pupils of the class. The totals at the bottom will furnish 
an interesting comparison of the ability of the pupils. Each 
pupil knowing his number can tell how he stands in relation 
to the other members of the class. If a new score card is 
posted each month, a pupil may see whether he is gaining 



ABILITY IN HANDWRITING 



219 



or losing in his position in the class. If he is losing, he will 
be inclined to seek the reason. He may see that his neatness 
has a low score. This furnishes a strong incentive for work 
to improve in neatness. Teachers and supervisors might 
compare their records. The use of the card may be varied 
by training pupils to score their own or others' handwriting, 
or by one teacher calling on another teacher to score the 
handwriting of his pupils. 

Standards. In Table XXII we give (1) standards pro- 
posed by Ayres for his "Gettysburg Edition"; (2) standards 
proposed by Freeman; and (3) "the Kansas Medians" 
which were obtained by using the directions given on page 
204. Table XXII is read thus: A second-grade class should 
have a median score for rate of 36 letters per minute, and 
a median score for quality of 44, when scored by the Ayres 
Scale. A third-grade class should have a median quality 
of 47 and a median rate of 48 letters per minute. The 
standards for the other grades are read in the same 
manner. 



Table XXH. Handwriting Standards — Rate in letters 

PER MINUTE — QUALITY IN TERMS OF THE AYRES SCALE 





School grades 




II 


in 


IV 


V 

55 
65 

50 
64 

55 
61 


VI 

59 

72 

54 

70 

59 
67 


VII 

64 

80 

58 
76 

64 

71 


vm 


Freeman standards — 

Quality 


44 
36 

38 
32 

44 
32 


47 
48 

42 
44 

47 
35 


50 
56 

46 
56 

50 
51 


70 


Rate 


90 


Ayres ("Gettysburg Edition") — 
Quality 


69 


Rate 


80 


Kansas medians — 

Quality 


70 


Rate 


73 







220 MEASURING THE RESULTS OF TEACHING 



Bate 



80 
76 
































p 




















72 

68 












A) 














/eT 








60 
56 
52 
48 














i 






























Q 


p 














































40 
36 
33 
28 






v« 




















































(g) 















34 38 



43 46 50 54 58 
Quality 



62 66 



Ayres's standards represented graphically. Ayres has 
represented graphically his standards for the "Gettysburg 
Edition" as shown in Fig. 33. Quality is represented on the 

horizontal lines and 
rate on the vertical. 
The positions of the 
small circles indi- 
cate the standards 
for the respective 
grades. This plan of 
graphical represen- 
tation is frequently 
helpful in interpret- 
ing the scores of a 
class or of a school. 
The basis of sat- 
isfactory standards 
in handwriting. The 
standards of attain- 
ment are determined 
by two considerations: (1) they must be attainable by 
pupils under ordinary school conditions, and without the 
expenditure of an unreasonable amount of time and effort; 
(2) they should be high enough to assure that the pupil 
will have sufficient skill in writing to meet the demands 
which will be made upon him. These considerations are 
emphasized by the facts that only a limited amount of 
time is available for the teaching of handwriting in the 
ordinary school, and that after practice has progressed 
for a time, it does not bring as large returns as it did in 
its initial period. 

The first of these considerations has been met by examin- 
ing the handwriting of thousands of children, gathered from 
all parts of our country. Freeman used the results of the 



Fig. 33. Graphical Representation op 
Ayres's Standards for the "Gettys- 
burg Edition" op his Handwriting 
Scale 



ABILITY IN HANDWRITING 221 

scoring of about five thousand specimens from each of the 
seven grades. These specimens were selected from a large 
number of specimens which were collected in fifty-six large 
cities of the United States. He found that the average of 
the scores of the upper half of these specimens gave scores 
for rate and quality which are approximately the standards 
he proposes. In checking up the second consideration, Free- 
man investigated the demands which are made upon those 
who are employed in several large commercial houses. The 
returns from this investigation, together with the results of 
the other investigation, indicated that the standards as pro- 
posed are but little more than the minimum essentials. 
Moreover, Freeman estimates on good evidence that these 
standards can be attained with an expenditure of not over 
seventy-five minutes a week. 

Standards required for practical work. Pupils are taught 
to write for two reasons: (1) in order to be able to meet the 
practical demands for writing outside of school, and (2) in 
order to be able to do the writing that is required in school, 
particularly in high school and college. Eventually these 
demands will determine the standards for both rate and 
quality. With reference to quality Ayres 1 and Ashbaugh 2 
have drawn certain conclusions from the requirements in 
handwriting which are set up by the examiners of the Muni- 
cipal Civil Service Commission of New York City. Ash- 
baugh quotes a letter from the Acting Director of the com- 
mission as follows: 

I find that the Municipal Civil Service Commission of New York 
ordinarily uses the standard of 70 per cent as a passing grade in 
handwriting, but for positions where handwriting is a special 
requirement the standard is sometimes set at 75 per cent. 

1 Ayres, L. P., A Scale for Measuring the Quality of Handwriting of 
Adults. (Russell Sage Foundation, Bulletin E 138.) 

2 Ashbaugh, Ernest J., Handwriting of Iowa School Children. (Bulletin 
of the University of Iowa, March 1, 1916.) 



222 MEASURING THE RESULTS OF TEACHING 

Ayres has shown that the ratings of 70 per cent and 75 per 
cent, as given by the commission, correspond respectively 
to scores of 40 and 50 on the Ayres Scale. Since this com- 
mission recommends many persons who cannot write better 
than the 40 specimen of the Ayres Scale, and recommends 
others who write only as well as the 50 specimen, for posi- 
tions where handwriting is a special requirement, it would 
follow that an ability to write as well as 50 on the Ayres 
Scale would be sufficient for all the demands which most 
pupils will meet. 

Koos 1 has recently reported a study of the non- vocational 
handwriting of 1053 persons and also the handwriting of sev- 
eral vocational groups. He states his conclusions as follows: 

To write better than 60 is to be in a small minority (13.5 per 
cent of 1053 cases) as concerns handwriting ability. Moreover, 
four-fifths of 826 judges consider the quality 60 adequate with a 
generous majority approving quality 50. In the light of these 
facts, it is difficult to see why, for the use under consideration (non- 
vocational correspondence) a pupil should be required to spend time 
to learn to write better than quality 60. There is even considerable 
justification for setting the ultimate standard at 50. As this demand 
touches every member of society, all children in the schools should be 
required to attain the standard set. 

From the facts that have been presented touching the ability 
in handwriting of persons engaged in various occupations, it seems 
to the writer that the quality 60 on the Ayres Measuring Scale for 
Adult Handwriting . . . is adequate for the needs of most vocations. 
, . . For that large group who will go into commercial work, for teleg- 
raphers, and for teachers in the elementary schools it will be necessary 
to insist upon the attainment of a somewhat higher quality, but hardly 
in excess of the quality 70. 

Standards required for school work. We have but little 
data on this point, but many pupils come to high schools 

1 Koos, L. V., "The Determination of Ultimate Standards of Quality 
in Handwriting for the Public Schools"; in Elementary School Journal 
(February, 1918), vol. 18, p. 422. 



ABILITY IN HANDWRITING 223 

unable to write rapidly enough for the demands placed upon 
them. They then often sacrifice the quality of their hand- 
writing for the sake of greater rate. Lewis 1 examined the 
hand-writing of 1760 third- and fourth-year students of 166 
Iowa Normal Training High Schools. He found their median 
score for quality to be 59.1 on the Ayres Scale, with a range 
from 34 to 89. Fifty per cent of the scores fell between 53.6 
and 64.3. The average rate of their handwriting was 90 
letters per minute. Thus, they rank with the seventh-grade 
standard for quality, and the eighth-grade standard for rate. 
Comparing their scores with those of eighth-grade children 
(see Table XXII), these high-school pupils write from ten 
to fifteen letters per minute faster, but no better than the 
average eighth-grade pupil. These data bear out the state- 
ment that the higher schools require greater rate of hand- 
writing than the training of the elementary schools have 
furnished. Therefore, increased emphasis should be placed 
upon rate in teaching handwriting. 

Summary. This discussion of standard scores for hand- 
writing may be summarized by saying that there is evidence 
that the standards for quality given in Table XXII may 
be slightly higher than they should be, particularly those 
given by Freeman. The standards given by Ayres may be 
considered satisfactory. In the case of the rate of writing 
Freeman's standards are probably the best. 

Types of situations revealed by the measurement of 
handwriting ability. Three types of situations which need 
corrective instruction may be recognized: (1) the median 
rate of writing is below standard; (2) the median quality is 
below standard; (3) the scores are too widely scattered. 

Type I. Below standard in rate of writing: The Cause. 

1 Lewis, E. E., "The Present Standard of Handwriting in Iowa Normal 
Training High Schools"; in Educational Administration and Supervision 
(December, 1915), vol. 1, pp. 663-71. 



224 MEASURING THE RESULTS OF TEACHING 

Fig. 34 represents the distribution of scores for a third- 
grade class. The numerals along the bottom of the figure 
denote quality on the Ayres Scale, and the rate in terms of 
letters written in one minute. The numerals along the side 
indicate the number of pupils. A perpendicular solid line 
shows the location of the median for the class, and a per- 
pendicular broken line shows the location of the standard 







M 














iS 

i 

i 



20.' 30 40 
Quality 



50 




40 50 60 70 



Fig. 34. Showing the Distribution of Scores in Hand- 
writing of a Third-Grade Class. 

The line M indicates the median score for the class, the line S the stand- 
ard for the class. 



for that grade. This class is below standard in both rate 
and quality. The quality will be considered under Type II. 
When the median rate of writing of a class is conspicuously 
below standard, as is the case of the third-grade class shown 
in Fig. 34, it is almost certain that the teacher is failing to 
place sufficient emphasis upon rate in his instruction. The 
author has found teachers and even supervisors of hand- 
writing who admitted that they had given no attention to 
the rate of writing, but it was obvious that rate was impor- 
tant as well as quality. A few pupils are very slow in their 
movements, and this may account for the low rate of indi- 
vidual pupils, but not for a low median score except in very 
unusual cases. 

The corrective. In considering corrective instruction for a 
class whose median rate score is below standard, it is neces- 



ABILITY IN HANDWRITING 225 

sary to bear in mind the relations which exist between rate, 
movement, rhythm, and quality. Investigation 1 has shown 
that the kind of movement, finger, arm and finger move- 
ment combined, or arm movement, does not affect the rate 
of writing when it is carried on for only a short time as is the 
case in the measurement of ability in handwriting. The 
apparent greater ease of production of arm or muscular 
movement may result in greater rate if rate is measured 
during a long period of writing. 

Nutt has recognized what he calls "rhythm." This is a 
quality or characteristic of the movement. It increases with 
age, but has no relation to amount of arm movement or to 
the quality of the writing. Nutt found that rate of writing 
and rhythm increase together; that is, children who score 
high in rhythm also score high in rate, but may not use arm 
movement or produce a better quality of handwriting than 
other children. 

Relation between rate and quality. Several studies have 
sought for a relation between rate and quality of hand- 
writing. In the Cleveland Survey 2 it was found that "in 
general speed and quality vary inversely. But there is a 
middle series of speeds and qualities where improvement 
in one does not seem to interfere with the other"; that is, 
outside of the limits which are approximately those of the 
proposed standards, efforts to secure an unusual degree of 
quality will reduce the rate, and vice versa. Several inves- 
tigations of adults' handwriting show that they tend to 
increase the rate and reduce the quality. A general view 
of the results bearing on this point shows that the children 
who write a good quality on the average write as rapidly 
as those who write a poorer quality. This seems to be due 

1 Nutt, H. W., "Rhythm in Handwriting"; in Elementary School Jour- 
nal, vol. 17, pp. 432-45. 

2 Judd, C. H., Measuring the Work of the Public Schools, pp. 80-81. 



226 MEASURING THE RESULTS OF TEACHING 

to the natural rhythm of the children. If this rhythm is 
forced or disturbed unduly the quality suffers. Thorndike's 
results indicate that causing a pupil to write more slowly 
than his normal rate did not improve the quality of the 
handwriting. 

Drills for increasing the rate of writing. Since within 
limits the rate of writing may be increased without seriously 
disturbing the quality, it will be possible in some cases to 
bring the median rate up to standard by rate drills in which 
the pupils are caused to write at standard rates. A con- 
venient device for doing this is represented by the following 
example. This is a dictation exercise arranged for the sixth 
grade. The rate of dictation which is indicated by the num- 
bers printed above the words is based upon Freeman's 
standards. (See page 219.) The teacher should direct the 
class to be ready to write, then, watching the second-hand 
of his watch, until it is at 60, start to dictate. A little pre- 
liminary practice will make it easy to dictate the words so 
that they will be pronounced as indicated. For example, the 
teacher should be pronouncing the word "care" just before 
the second-hand reaches the ten-second mark, etc. 

5 10 20 30 

Do you take care to keep your teeth very clean, by washing 

40 50 60 15 

them without failing every morning and after every meal? This 

20 30 40 50 60 

is very necessary both to preserve your teeth a great while, and 

10 20 

to save you a great deal of pain. (Stop.) 

At first a class will not be accustomed to this form of 
exercise and may not respond in a satisfactory manner, but 
a little patience on the part of the teacher will soon elimi- 
nate such temporary confusion. The rate of a class which 
is far below standard should be gradually increased. For 
example, if the sixth-grade class is below the fourth-grade 



ABILITY IN HANDWRITING 



227 



standard, a dictation exercise arranged for the fourth 
grade should be used. When the class is able to respond to 
this satisfactorily, the dictation exercise for the fifth grade 
should be used and later the one for the sixth grade. 

If the quality of the handwriting of certain pupils de- 
creases because of such drills, these pupils should be excused 
from them or a different type of drill used. The following is 
a modification which will be helpful in such cases; the sen- 
tence, "The quick brown fox jumps over the lazy dog" 
contains thirty-five letters. 

8th-grade pupils should write this 11 times in 4 min. 



7th 


<< 


" 


" " 


" 


8 ' 


. « 3 


« 


30 


6th 


<« 


<< 


M « 


" 


6 ' 


' "3 


M 




5th 


« 


" 


" " 


" 


5 ' 


« « 2 


(« 


45 


4th 


« 


" 


" " 


« 


4 * 


< « 2 


" 


30 


3d 


« 


" 


« « 


" 


3 ' 


« « 2 


K 


10 


2d 


« 


« 


« <« 


*i 


2 ■ 


' "2 


K 





The pupils should memorize the sentence and write it 
several times for practice and for spelling. The teacher 
should then time their writing. Those who do not write the 
required number of letters in the allotted time, as given in 
the table above, should be told to write faster, until they 
have done the test successfully. 

Developing rhythm. If such exercises as described above 
reveal a serious sacrifice in the quality when the rate is in- 
creased, or if the pupil's handwriting cannot be brought up 
to standard rate, we may consider that the pupil's rhythm 
has not developed to the place where it will sustain this 
rate. Since we do not know which is the primary factor, 
rhythm or rate, the best procedure would be to seek to 
develop both. Rhythm may be increased by the use of 
music. If the school owns a phonograph, records suitable 
for use in penmanship classes may easily be secured. The 
time of the music may be adjusted to the grade. Careful 



228 MEASURING THE RESULTS OF TEACHING 

attention to the securing of a free, well-relaxed hand posi- 
tion will aid in securing rate. Sometimes a careful analysis 
of letter forms will reveal that the pupil is forming some 
letters in a way that makes a satisfactory rate impossible. 
In such cases new forms of those letters should be taught. 

Type II. Below standard in quality of writing. This con- 
dition may occur along with an unsatisfactory rate, as in 
Fig. 34, or when the rate is up to or above standard. In 
attempting to increase the median quality of the handwrit- 
ing of a class, methods and devices used should be selected 
in the light of facts which have been established by investi- 
gations of the learning process, 1 as it occurs in learning to 
write. There are not sufficient data from comparative studies 
of different penmanship systems to establish any single sys- 
tem as superior to others in its effectiveness to secure results 
in terms of rate and quality of handwriting. Hence, the cor- 
rective to be sought is not some system of writing which is 
a panacea for all handwriting troubles. 

General laws of learning applied. The ability to write 
well is a habit; hence, the laws of habit formation apply to 
the acquisition of this ability. 

The first essential factor is a right start. The pupil must 
have a clear view of the habit to be acquired. This may 
mean a definite idea of the movement to be executed, or a 
picture of the letters or series of letters which are to be made. 
The start must be made with a strong initiative. Sometimes 
the pupil must be shocked into a desire to correct a fault of 
his handwriting. 

The second essential is that of attentive repetitions. The 

1 No attempt is made to review or to criticize the material which ap- 
pears in numerous manuals of handwriting. Much excellent material which 
appears in The Teaching of Handwriting, by Freeman, is not even men- 
tioned, because of lack of space. The difficulty of confining this discussion 
to the actual facts discovered through measurement of handwriting will 
be apparent. 



ABILITY IN HANDWRITING 229 

repetitions or drills should be strongly motivated. All inves- 
tigations of habit formation agree upon this point. The 
periods of practice are most efficient if not carried to the 
point of fatigue; hence, for the lower grades Freeman sug- 
gests frequent ten-minute periods of practice. In no grades 
should the periods be longer than twenty minutes. 

The third step, as often stated, is, "Allow no exceptions to 
occur." If a pupil practices correct form in the penmanship 
class for ten minutes, and then uses poor form in a spelling 
class for the same length of time, the latter exercise will 
tend to cancel the effects of his practice in the penmanship 
class. 

A fourth step is the repetition of the habit until it is well 
fixed. This means that the repetitions must extend beyond 
the point of apparent completion to permanent automatism. 
After this stage is reached, incentives should be found 
which will raise the habit from the level of mere automatism 
to higher levels of skill. 

Motivating practice. A number of devices and plans have 
been proposed for the motivation of practice in correcting 
faults in quality of handwriting. Wilson 1 gives the result 
of an interesting experiment in which the Thorndike Scale 
was used in such a way that the students could follow their 
own progress in handwriting. In this case each student was 
competing with his own record. Several teachers have 
constructed scales from the specimens collected in a school 
or class. These scales may be constructed by rating the 
specimens with any one or more of the scales described. 
Superintendent Bliss of the Montclair, New Jersey, schools 
is quoted by Wilson as follows: "A scale made from the 
writing of pupils makes a stronger appeal than either the 
Ayres or Thorndike Scales." A scale, either one made from 

1 Wilson and Wilson, The Motivation of School Work (Houghton Mifflin 
Company, 1916), p. 187. 



230 MEASURING THE RESULTS OF TEACHING 

specimens collected in the school or one of those described 
on page 208, should be posted in the schoolroom and pupils 
encouraged to compare their handwriting with it frequently. 
For this purpose the Ayres Scale is most convenient. 

Charters l recommends a "writing hospital" to which the 
poor writers are sent until they are properly convalescent. 
This hospital is a special penmanship class. Stone 2 has a 
plan which puts all the pupils of a school in four groups for 
their writing lessons. These are groups 1, 2, 3, and the 
excused group. The special feature of this plan is that at 
stated intervals members of a lower group are allowed to 
challenge members of a higher group, and a contest for the 
coveted place ensues. 

Many special devices for motivation are in use. Pupils 
write letters ordering supplies for the school, or they write 
invitations to school parties, pageants, etc. Some pupils 
write letters for the teacher or principal. 

M. 
IS 



tt£J 



20 30 .40 BO 60 70 20 30 40 50 60 70 80 90 100 
Quality Speed 



Fig. 35. Showing the Distribution of Scores in Handwriting op 
Fourth-Grade Class 

The line M indicates the median score for the class, the line S the standard for the class. 

Type HI. Scores too widely scattered. The scores of a 
fourth-grade class of this type are shown in Fig. 35. As in 
the case of other school subjects, the pupils who are grouped 
together in any school grade will be found to differ widely 

1 Charters, W. W., Teaching the Common Branches. (Houghton Mifflin 
Company, 1916.) 

2 Stone, C. R., "Motivation of the Formal Writing Lesson Through a 
Special Classification of Pupils for Writing"; in Scliool and Home Education, 
June, 1915. 



ABILITY IN HANDWRITING 



231 



in both rate and quality. However, these differences should 
be reduced to a minimum. Fig. 36 represents the scores of 
a fifth-grade class which exhibits what probably should be 
regarded as a satisfactory condition. The differences be- 
tween the members of this class are much less than those of 
the class shown in Fig. 35. 



MliS 





Fig. 36. Showing the Distribution of Scores in Handwriting 
of Fifth-Grade Class 

The line M indicates the median score for the class, the line S the standard for 
the class. 



In connection with his "Gettysburg Edition," Ayres has 
given standard distributions for the four upper grades. 
These are reproduced in Fig. 37. The teacher may use them 
to ascertain whether or not the scores of his class are too 
widely scattered. 

Correctives. The reduction of a high degree of individual 
differences is largely a matter of dealing with individual 
pupils. A reclassification may be wise where it is possible, 
but for the most part the classification of pupils is deter- 
mined by their standing in other subjects. Those pupils 
who are distinctly above the eighth-grade standard should 
be excused from the penmanship class. They may spend 
the time thus saved upon other subjects. Dictation exer- 
cises, such as described on page 226, will tend to reduce the 
degree of individual differences in rate of writing. 

Diagnostic measurements. In the case of pupils who are 
below standard in quality, it is helpful to diagnose their 





ad 


3o 

W M 






«■ 



1 




ABILITY IN HANDWRITING 



233 



handwriting using either Freeman's Scale or Gray's Score 
Card. This will give the teacher a statement of the particu- 
lar defects which exist and this information will provide a 
basis for prescribing corrective instruction. As typical of 
this procedure we quote the following: 1 

A detailed analysis of the faults which appear in the child's 
writing and of the adjustments which are necessary to correct them 
has been worked out by Mr. C. W. Reavis, Principal of the Laclede 
School, St. Louis, Missouri, on the basis of his experience in super- 
vision, and is here presented with his permission. 



Analysis of Defects in Writing and their Causes, in use by 
Principal Reavis 

Cause 

1. Writing arm too near body. 

2. Thumb too stiff. 

3. Point of nib too far from fingers. 

4. Paper in wrong position. 

5. Stroke in wrong direction. 



Too much slant 



Writing too straight 



1. Arm too far from body. 

2. Fingers too near nib. 

3. Index finger alone guiding pen. 

4. Incorrect position of paper. 



Writing too heavy 



1. Index finger pressing too heavily. 

2. Using wrong pen. 

3. Penholder of too small diameter. 



Writing too light 



1. Pen held too obliquely or too straight. 

2. Eyelet of pen turned to side. 

3. Penholder of too large diameter. 



W T riting too angular 



1. Thumb too stiff. 

2. Penholder too lightly held. 

3. Movement too slow. 



1 Freeman, F. N., The Teaching of Handwriting (Houghton Mifflin Com- 
pany), pp. 71-72. 



234 MEASURING THE RESULTS OF TEACHING 

1. Lack of freedom of movement. 
Writing too irregular 2. Movements of hand too slow. 

3. Pen gripping. 

4. Incorrect or uncomfortable position. 

1. Pen progresses too fast to right. 
Spacing too wide 2. Too much lateral movement. 

QUESTIONS AND TOPICS FOR STUDY 

1. A teacher may judge the handwriting of his class by watching the 
pupils while they write or by examining the specimens which they 
have written. Which is the better method if the purpose is to make 
comparisons of classes? Which is better for discovering the hand- 
writing defects of individual pupils? What factors would you keep in 
mind in watching children while they write? What factors in the 
other method? 

2. Ask a class to write the three sentences from Lincoln's Gettysburg 
Address. Direct them to start together and write as rapidly as they 
can for one minute. At the end of one minute stop them and direct 
them to record the number of letters they have written. Then ask 
them to begin again and write for one minute writing as well as they 
can. If you wish to eliminate practice effects, repeat the experiment, 
again reversing the order of the directions. Note the difference in 
the rates due to the nature of the directions. 

3. Select ten or preferably one hundred specimens of handwriting and 
rate them every day for several days by means of the scale you have. 
Keep the record of your day's rating, but do not use them to help you 
in making future ratings. After several ratings note the consistency 
of your ratings. 

4. Use the Gray Score Card (or Freeman Scale) in scoring the poorer 
specimens of handwriting. Prescribe the drills you would use in cor- 
recting these defects. Compare this with the recommendations of 
other teachers or students. Try your prescription on the pupils con- 
cerned if possible. 

5. For what purpose would you use the dictation exercises? 

6. Select a defect of letter formation frequently found in a pupil's hand- 
writing. Direct the pupil's attention to this defect and challenge him 
to correct it. Direct that a record be taken as follows: If the defect 
were found in letter "a" instruct the pupil to count the number of 
such errors to be found in fifty consecutive "a's" as they occur in his 
handwriting written prior to the time you pointed out the defect. 
After a period of practice, direct the pupil to make another counting 
from his handwriting written at some period other than the writing 
period. 



CHAPTER IX 

THE MEASUREMENT OF ABILITY IN LANGUAGE AND 
GRAMMAR 

The measurement of ability to write compositions. The 
plan for measuring the ability of pupils to write composi- 
tions is very similar to that used for handwriting. Compo- 
sition scales have been devised which consist of a number 
of compositions arranged in order of merit, and a pupil's 
composition is measured by "matching" it with the com- 
position of the scale which most nearly equals it in merit. 
As in the case of handwriting, care must be exercised in 
securing compositions from pupils. The first draft of a 
composition is frequently inferior to the form obtained 
when it has been rewritten. Also there will probably be a 
difference between compositions written as a class exercise 
and compositions prepared as home work. 

The Willing Composition Scale for measuring composi- 
tions written as a class exercise. Willing 1 has devised a 
scale which consists of compositions written as a class exer- 
cise. The topic was "An Exciting Experience." Several 
particularly exciting experiences were suggested by the 
teacher and the pupils were allowed twenty minutes for 
writing. The compositions were rated both for form (errors 
in spelling, punctuation, capitalization, and grammar) and 
for "story value." Those chosen for the scale increase grad- 
ually in both form and "story value." The scale is repro- 
duced here so that teachers may understand better this 
type of measuring instrument in the field of composition. 

1 Willing, M. H., "The Measurement of Written Composition in Grades 
IV to VIII"; English Journal (March, 1918), vol. 7, p. 193. 



236 MEASURING THE RESULTS OF TEACHING 

Willing Scale for Measuring Written Composition 

(The values: 90, 80, 70, 60, 50, 40, 30, and 20 given the respec- 
tive samples are arbitrary and merely for practical convenience. 
20 means 15 to 24.9, 30 means 25 to 34.9, etc.) 

20 

Deron the summer I got kicked and sprain my arm. And I was 
in bed of wheeks And it happing up to Washtion Park I was go- 
ing to catch some fish. And I was so happy when I got the banged 
of I will nevery try that stunt againg 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 30. 

30 

The other day when I was rideing on our horse the engion was 
comeing and he got frightened so he through me down and I broke 
my hand. 

And the next thing I done was I went to the doctor and he put 
some bandage on it and told me to come the next day so I came 
the next day and he toke the bandage off and he look at it and then 
it was better. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 23. 

40 

My antie had her barn trown down last week and had all her 
chickens killed from the storm. Whitch happened at twelve oclock 
at night. She had 30 chickens and one horse the horse was saved 
he ran over to our house and claped on the dor whit his feet. When 
we saw him my father took him in the barn where he slepped the 
night with our horse. When our antie told us about the accident 
we were very sorry the next night all my anties things were frozen. 
The storm blew terrible the next morning and I could not go to 
school so I had to stay home the whole week. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 17. 



ABILITY IN LANGUAGE AND GRAMMAR 237 

50 

One time mother and father were going to take sister and I for 
a long ride thanksgiving, We had to go 60 miles to get there, When 
sister and I herd about it we were very glad. It was a very cold 
trip. We four all went in a one seated automobile. Dady drove 
and mother held me and sister sat on the top the top was down. 
Mother could not hold sister for she was two heavy. When we 
got there they had a hot fire ready for us and a goose dinner. We 
were there over night. In the morning it was hot out. This was 
on a farm. Sister and I got to go horse-back riding. It was lots of 
funs. They had children. The children were very nice. Our trip 
home was very cold. When we got home it had snod. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 14. 

60 

One time when mother, some girl friends and myself were 
staying up in the mountains. An awful storm came up. At the 
we were way up the mountain. The lightning flashed and the 
thunder roared. We were very frightened for the cabin we were 
staying at was at the foot of the mountain. We did n't have our 
coats with us for it was very warm when we started. There were 
a few pine trees near us so we ran under them. They did n't do 
much good for the rain came down in torrents. The rain came 
down so hard that it uprooted one of the trees. Finely it began to 
slack a little, So we thought we would try and go back. About 
half way down the mountain was a little hut. We started and when 
got about half way down it began to rain all the harder. We did n't 
know what to do for this time there was n't any trees to get under. 
We decided to go on for the nearest shelter was the hut. Finely we 
got there cold and wet to the skin. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 11. 

70 

When I was in Michegan I had an exciting thing happen or 
rather saw it, it was when the big steamship plying between Chi- 



238 MEASURING THE RESULTS OF TEACHING 

cago and Muskegon was sunk about 7 o'clock in the evening. It 
caught on fire with a load of cattle and products from the market 
on board, one of the lifeboats carrying some of the people who were 
on board landed at our pier. The "Whaleback" steamer which 
goes between Chicago and Muskegon was two hours later in coming 
than the freighter and was stopped to clear up the wreckage, all 
of the cattle and products and an immense cargo of coal were lost, 
but there were only two people lost, the ship tried hard to get to 
port with her cargoe but, could not reach it. The next morning 
we found planks, and parts of the wreck on the beach. Our cottage 
was at the top of a cliff and it was just one hundred feet to the lake 
from our cottage, we had a beautiful view, and the sight of the fire 
on the horizon was a beautiful sight (though it was pitiful). 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 8. 

80 

Near our ranch in Fort Logan there was a chicken ranch. One 
day my sister and I went up to the chicken ranch on our horses. 
Coming back there was a road leading from our house to the main 
road and along this road were half rotted stumps. On every one 
of these stumps what do you think we saw. We saw snakes ! snakes ! 
snakes! I suppose these snakes were shedding their skins, they 
were of every color, shape, and size. But when sister and I saw 
these snakes we whipped our horses into a gallop and away we 
went just as hard as we could go. When we got to the house we 
went in and mamma could n't get us out of the house that day. I 
was so scared that I believe I dreamed about snakes for a month. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 5. 

90 

The most exciting experience of my life happened when I was 
but five years of age. I was riding my tricycle on the top of our 
high terrace. Beside the curbing below, stood a vegetable wagon 
and a horse. Suddenly I got too near the top of the terrace. The 
front wheel of my tricycle slipped over and down I went, licety- 
split, under the horse standing by the curbing. I had quite a high 



ABILITY IN LANGUAGE AND GRAMMAR 239 

tricycle and the handlebars scraped the horse's stomach, making 
him kick and plung in a very alarming manner. I was directly 
under him during this, but finally rolled over out of his way and 
scrambled up. I looked at my hands ! Most of the first finger and 
part of the thumb of my left hand were missing. The horse had 
stepped on them. I had endured no sensation of pain before this, 
but now my mangled hand began to hurt terribly. I was hurried 
to the hospital and operated on, and now you would hardly notice 
one of my fingers is missing. I certainly have good cause to con- 
gratulate myself on my good fortune in escaping with as little in- 
jury to myself as I did, for I might have been terribly mangled in 
my head or body. 



Number of mistakes in spelling, punctuation, and syntax per 
hundred words, 0. 

Directions for using Willing's Scale for Written 
Composition 

In using the Composition Scale, these directions should be fol- 
lowed carefully because the compositions were written by school 
children who followed these same directions. 

1. The teacher should make certain that all pupils are provided 
with good pen points and ink, or well-sharpened pencils if pencils 
are to be used. Have distributed to each pupil two sheets of 
theme paper (approximately 8 \ by 11). It is best to use theme 
paper which has printed at the top the suggested list of topics. 
If this kind of paper is not used, the teacher must write the fol- 
lowing list of topics on the blackboard: 

An exciting experience. 

A storm. 

An accident. 

An errand at night. 

A wonderful story. 

An unexpected meeting. 

In the woods. 

In the mountains. 

On the ice. 

On the water. 

A runaway. 



240 MEASURING THE RESULTS OF TEACHING 

2. The teacher should then say to the pupils: "I want you to 
write me a story. It is to be a story about some exciting experience 
that you have had, about something or other very interesting that 
has happened to you. If nothing of the sort has ever happened 
to you, then tell me of an exciting experience some one you know 
has had. You may even make up a story of this kind, if you have 
to, though I believe you will do better, on the whole, with a real 
one. I am going to give you about twenty minutes in which to 
write. You are to write on both sides of the paper, to do all the 
work yourselves, and to ask no questions at all after you begin. 
You may make whatever corrections you wish between the lines. 
There will be no time to rewrite your story. 

"The general subject together with some suggestions is printed 
at the top of the paper on which you are to write. (I have written 
the general subject on the blackboard, together with some sug- 
gestions.) You do not have to write on any of these topics unless 
you want to; they are merely to help out in case you cannot think 
of an exciting experience yourself. You may begin now as soon 
as you wish." 

3. Allow opportunity for asking questions and make an effort 
to put the children at ease. Allow full twenty minutes for the 
actual writing. At the end of this time say to the pupils: 

"You are to have four or five minutes in which to finish your 
stories; make corrections and count the number of words written. 
Write this number at the end of your story, write also your name, 
age, and grade.'* 

At the end of five minutes collect the papers. 

It is important that the pupils be not allowed to correct their 
compositions, except such corrections as they may make during 
this period of four or five minutes. The teacher must remember 
that it is this type of composition which was used in making the 
scale and establishing the standards. 

4. In rating the compositions by means of the scale, two quali- 
ties are recognized: (1) "story value" and (2) "form value." The 
composition should be rated for "story value" first. 

Rating for "Story Value" Read the compositions, neglecting 
all errors of grammar, punctuation, capitalization, and spelling, 
and keeping in mind only the value of the story which the pupil 
is telling. As the compositions are read, sort them into piles, 
placing in one pile those which most nearly resemble in "story 



ABILITY IN LANGUAGE AND GRAMMAR 241 

value" composition 20 of the scale; in another pile those which 
most nearly resemble composition 30; in another pile those which 
most nearly resemble composition 40; and so on for the other 
compositions of the scale. 

After this is done, compare the compositions in each pile with 
each other, in order to make sure that the rating has been done 
correctly. Make any adjustments which you think should be 
made. Mark each composition with the value of the scale com- 
position which it most nearly resembles. In case you believe that 
the true "story value" of the pupil's composition lies between 
that of two of the scale compositions, the interpolated marks 25, 
35, etc., may be used. 

Rating for "Form Value." After the compositions have been 
rated for "story value," carefully mark all errors in grammar, 
punctuation, capitalization, and spelling. Count these errors and 
multiply the total by 100. Divide this number by the number of 
words in the composition. This quotient is the number of errors 
per hundred words. 

The quotient found, as directed above, and the "story value" 
of the composition constitute the pupil's score. These scores are 
valuable to the teacher. They show the standing of each pupil 
in two respects. They tell the teacher whether the pupil needs to 
give attention to the "form" of his writing (grammar, punctuation, 
capitalization, and spelling) or to the "story value," or to both. 

Recording the scores. For recording the scores the record sheet 
shown in Fig. 38 is used. Sort the compositions for a class into piles 
according to their "story value." (By a class we mean the pupils 
who belong to the same grade and who recite together. If a teacher 
has a class composed of pupils belonging to two grades — say some 
belonging to 5 A and some belonging to 6 B — it will be neces- 
sary to make two tabulations.) 

If interpolated values have been used, they should be grouped 
according to the explanation of the scale value which is given 
at the top of the scale. 

Take the compositions whose "story value" is 20. These are 
to be listed in the first column of the table in the space which cor- 
responds to their "form value." For example, in the first space 
of this column record the number of these compositions whose 
"form value" is between and 2.9; in the second space record 
the number of compositions whose form value is between 3 and 



242 MEASURING THE RESULTS OF TEACHING 



Class Record Sheet 



City School . 



.Grade. 





Errors per Hundred Words 


Story value 




20 


30 


40 


50 


60 


70 


80 


90 


for Errors 


Oto 2.9 


















3to 5.9 




















6 to 8.9 




















9 to 11.9 




















12 to 14.9 




















15 to 17.9 




















18 to 20.9 




















21 to 23.9 




















24 to 26.9 




















27 to 29.9 




















Above 30 





























































Class Medians. Form value Story value . 



Fig. 38. Showing Class Record Sheet fob use with Willing' 
Composition Scale 



ABILITY IN LANGUAGE AND GRAMMAR 243 

5.9; in the third space record the number of compositions whose 
" form value " is between 6 and 8.9, etc. After the compositions 
in each pile have been recorded in this way, the number of com- 
positions recorded on each line should be counted and the total 
entered in the total column. The same should be done for the 
compositions entered in each column. 

Finding the class scores. The median score for form value 
may be found by arranging the compositions in order of the 
form scores and taking the score of the middle composition. 
In case there is an even number of papers, the average of 
the scores on the two middle ones should be taken. The 
median score for "story value" may be found in the same 
way. The median scores may also be calculated from the 
distributions by following the directions given on page 103. 

Tentative standards. Tentative standards for Willing's 
Composition Scale are given in Table XXIII. It will be 
noticed that the median scores for Denver are conspicuously 
below those for five Kansas cities. This may be due to the 
fact that reports have been received from only a few cities. 

Table XXTU. Median Scores for Willing's Composition 

Scale 



Grade 


Denver 


Five Kansas cities 


Story value 


Form value 


Story value 


Form value 


IV 


32 
43 
50 
60 
63 


22 
16 
14 
11 
10 


44 
58 

75 
77 
82 


12 


V 


10 


VI 


5 


VII 

VIII 


5 
6 







Other scales for measuring written composition. A scale 
called the Nassau County Supplement has been devised by 
Trabue. It consists of nine compositions, seven of which 



244 MEASURING THE RESULTS OF TEACHING 

were written by elementary-school pupils on the topic, 
"What I should like to do next Saturday." It is designed to 
measure only "story value" of compositions. Copies of 
this scale may be obtained from the Bureau of Publications, 
Teachers College, Columbia University, New York City. 

The Hillegas Scale consists of ten compositions ranging 
from an artificial production whose scale value is zero to the 
tenth composition whose scale value is 9.3. Three of the 
ten compositions are artificial productions, five were written 
by high-school pupils, and the remaining two by college 
freshmen. No two were written on the same topic and they 
vary greatly in length and type. In the Thorndike Extension 
of the Hillegas Scale, only a few of the compositions of the 
original scale have been used and several compositions are 
given for each degree of merit in the middle of the scale. 
Twenty-nine compositions represent fifteen degrees of merit 
within approximately the same range as the original scale. 
This makes a more finely divided scale than the original one. 
Copies may be obtained from the Bureau of Publications, 
Teachers College, Columbia University, New York City. 

The Harvard- Newton Composition Scale consists of four 
separate scales, one for each form of discourse; argumenta- 
tion, description, exposition, and narration. Each of the 
scales consists of six compositions written by eighth-grade 
pupils and arranged in order of merit as determined by the 
marks assigned by teachers rating them as eighth-grade 
compositions. For each composition there is given a state- 
ment of the most significant merits and defects. Copies of 
the scale may be secured from the Harvard University Press, 
Cambridge, Massachusetts. 

The compositions used by Breed and Frostic 1 in deriving 

1 Breed, F. S., and Frostic, F. W., "A Scale for Measuring the General 
Merit of English Composition"; in Elementary School Journal, vol. 17, 
pp. 307-25. 



ABILITY IN LANGUAGE AND GRAMMAR 245 

their scale were written by sixth-grade pupils under uniform 
conditions. A part of the story called "The Picnic" was 
read to the class and they were given twenty minutes to 
complete it. The method of selecting compositions for the 
scale and determining scale values was similar to that em- 
ployed by Hillegas. 

The measurement of ability in English Grammar. Char- 
ters^ Diagnostic Test in Language and Grammar for Pro- 
nouns. Charters collected more than twenty-five thousand 
errors that pupils make in using pronouns in their oral 
language. These were classified under forty heads; that is, 
there were only forty different kinds of errors in the use of 
pronouns in the total twenty-five thousand. The language 
part of the test consists of eighteen sentences. The pupils 
are required to write the correct form. This test is de- 
signed to be used in grades three to eight. In the grammar 
part of the test, which consists of twenty-four sentences, 
they are required to give the reason for making the correc- 
tion. The form of this test is illustrated by a few of the 
exercises given below. The amount of credit to be given 
for doing each exercise correctly has been determined. This 
test measures two abilities: (1) The ability to use correct 
forms of pronouns. The measure of this ability is his "lan- 
guage score" and is the sum of the values of the language 
exercises done correctly. (2) The ability to give the gram- 
matical rule which tells which form is correct. The measure 
of this ability is his "grammar score" and is the sum of 
the values of the grammar exercises done correctly. 

Recording the scores. For this purpose a class record 
sheet with detailed directions is furnished with the tests. 

Recording scores for purpose of diagnosis. In order to 
obtain a diagnosis of the abilities of the pupils of a class, 
the form of tabulation which is partly shown in Fig. 38 is 
helpful. It gives in a compact form the record of each pupil 



1.5 

ii 
I* 



II 
p 



3 



i 



j 



g 

o 
a 

Q 

1 
I 

3 

a 

§ 



w 



ABILITY IN LANGUAGE AND GRAMMAR 247 





Number of Exercises 


Name of 
pupil 


2 


3 


4 


5 




39 


40 


41 


42 


Total 




L 





/. 


Q 


L 





L 


Q 




L 


Q 


L 


<: 


L 


Q 


£ 





L 


a 


























































































































































































































































































































































































































































































































































































































Per cent 

























































































































Fig. 39. Record Sheet for Diagnosis 

Charters'a Diagnostic Test in Language and Grammar. Exercises 1 and 29 are omitted 
because they are correct sentences. 



248 MEASURING THE RESULTS OF TEACHING 

on each exercise. With this tabulation before him the 
teacher can determine (1) what errors should be given more 
emphasis and (2) what pupils are lacking in ability. Since 
the test includes all the pronoun errors, the teacher may- 
be sure that his pupils have been tested completely in this 
field. 

Standards. No standards are yet available for this test, 
but those desiring to use it may obtain the standards from 
the Bureau of Educational Research, University of Illinois, 
Urbana, Illinois, as soon as they have been determined. 

Starch's Punctuation Scale. Starch has devised a punctu- 
ation scale, which consists of a number of sentences which 
the pupil is to punctuate correctly. The sentences are 
grouped in exercises of gradually increasing difficulty of 
punctuation. The nature of the scale may be illustrated by 
the following extracts. The pupil's score is the value of the 
highest step which he does seventy-five per cent correct. 

Step 6 

1. We visited New York the largest city in America. 

2. Everything being ready the guard blew his horn. 

3. There were blue green and red flags. 

4. If you come bring my book. 

Step? 

1. I told him but he would not listen. 

2. Concerning the election there is one fact of much importance. 

3. The guests having departed we closed the door. 

4. The train moved swiftly but Turner arrived too late. 

Step 10 

1. A tall square building is located on State Street. 

2. Washington Irving whose personality was genial and charm- 
ing became very popular in England. 

3. You see John how I stand. 

4. On the path leading to the cellar steps were heard. 



ABILITY IN LANGUAGE AND GRAMMAR 249 

Step 13 

1. I saw no reason for moving therefore I stayed still. 

2. There are three causes poverty, injustice and indolence. 

Step 16 
1. As in warfare a band of men though strong and brave indi- 
vidually is collectively weak if it is not well organized so a 
speech a report an editorial an essay any composition though 
its parts may be forcible or clever is weak as a whole if it is 
not well organized. 

Standards. The following are tentative standards of 
attainment for the ends of the respective school years: 

Grade Score 

Seventh 8.0 

Eighth 8.3 

No diagnosis obtained. Starch's Punctuation Scale does 
not yield a diagnosis because he did not analyze the field of 
punctuation to determine the types of sentences requiring 
punctuation. In this respect, as well as in others, it differs 
from Charters's Diagnostic Test in Language and Grammar 
described above. 

Measuring accuracy in copying. Copying is a phase of 
school work which receives little explicit attention. This is 
probably due to the assumption that pupils are able to copy 
accurately because it appears to be such a simple activity. 
Copying bears a relation to written expression and to other 
school subjects as well. Themes are usually copied before 
being submitted to the teacher. In solving problems in 
arithmetic the quantities are copied from the text. In 
gathering information from references copying occurs. 

The Boston test. The following test of pupils' ability to 
copy printed matter was prepared by a group of Boston * 
teachers: 

1 Determining a Standard in Accurate Copying. (Boston Public Schools, 
English, School Document no. 2, 1916.) 



250 MEASURING THE RESULTS OF TEACHING 

Directions for Giving and Scoring the Test 

1. Read to the pupils the directions which are printed at the 
head of the selection they are to copy, but give them no 
further help. For example, do not specify possible errors 
which may be made. 

2. Pupils ought not to see the selection until they are ready to 
copy it. Hence it should be placed on the desk face down 
until the signal is given to begin work. 

3. Every error should be checked distinctly. 

4. The errors which were to be noted were as follows : In spelling, 
capitalization, punctuation, undotted "i's," uncrossed "t's"; 
in omitting words, in adding words, in wrong words used, and 
in misplaced words. 

Directions to Pupils 

Copy in ink as much of the following selection as you can copy 
accurately in fifteen minutes without hurrying. Accuracy is more 
important than speed: 

Lieutenant Ouless 

In this story a young British lieutenant, in a moment of extreme 
irritation, strikes a private soldier. The act is one that calls for 
dismissal from the Queen's service. What is the officer to do? He 
cannot send money to the soldier — who happens to be the redoubt- 
able Ortheris himself — nor can he apologize to him in private. 
Neither can he let matters drift. Ortheris, too, has his own code 
of pride and honor; he too is a "servant of the Queen"; but how 
is the insult to be atoned for? The way out of this apparently hope- 
less muddle is a beautifully simple one, after all. The lieutenant 
invites Ortheris to go shooting with him, and when they are alone, 
asks him "to take off his coat." "Thank you, sir!" says Ortheris. 
The two men fight until Ortheris owns that he is beaten. Then the 
lieutenant apologizes for the original blow, and the officer and pri- 
vate walk back to camp devoted friends. That fight is the moral 
salvation of Lieutenant Ouless. 1 

Kinds of errors made. This test was given to 4494 first- 
year pupils in the Boston High Schools in November, 1914, 
1 Bliss Perry, A Study of Prose Fiction. 



ABILITY IN LANGUAGE AND GRAMMAR 251 

and therefore may be considered to measure the ability of 
pupils completing the eighth grade. The results are both 
interesting and significant. The following is quoted from 
the Bulletin mentioned above: 

The errors noted consisted of nine different kinds, and the 
number of each kind made in this test by 4494 pupils is shown by 
the following tabulation: 

Spelling 5,829 

Capitalization 644 

Omitted words 4,077 

Added words 606 

Wrong words used 840 

Misplaced words 105 

Punctuation 5,876 

Undotted "i's" 8,794 

Uncrossed "t's" 606 

Total 27,377 

Average errors per pupil 5.54 

Misspelled words. The test consisted of 170 words, 105 of them 
different words. It is a notable fact that every word was mis- 
spelled by somebody. It is also interesting that 92.2 per cent of the 
words in the test are found in Jones's Concrete Investigation of the 
Material of English Spelling. 1 In spite of the fact that these are 
words commonly used by children in their writing, 11.8 per cent 
of them were misspelled more than 100 times. This does not mean 
that 11.8 per cent of the children missed these words, because one 
pupil might have missed the same word more than once. 

It is impossible to make any statement in regard to the average 
because many of the words occur in the selection more than once, 
and if misspelled by the same person each time it occurs it is 
counted more than one error. Some children spelled a word incor- 
rectly in one place and correctly in another. One boy spelled 
"lieutenant" wrong four out of five times, and spelled it a different 
way each time. Then, not all the children finished the entire selec- 
tion, and no record was kept of the exact number of words each 



Published by the University of South Dakota. 



252 MEASUKING THE RESULTS OF TEACHING 

wrote. However, 4494 pupils taking the test made 5829 errors in 
spelling alone, the number of errors for each word varying from 
1 to 1045. 

Undotted "i's" and uncrossed "fs." The errors made by leaving 
the "iV undotted and the "t's" uncrossed comprise about one 
third of the entire number of errors and are largely important be- 
cause of their value to legibility, as pointed out by Ayres. In con- 
nection with these errors, it is very noticeable that most of them 
were confined to comparatively few pupils. If a child showed a 
tendency to dot his "i's" and cross his "t's" in the first few lines, 
the chances were that that individual would have but few errors. 
On the other hand, if the child made many errors in the first part 
of the paper, there were many throughout the copying. One boy 
went through the entire paper without dotting an "i." Many 
others dotted only a small part of them. 

The same test was given in Kansas City, Missouri, to 
the pupils in the seventh grade and in the first year of the 
high school. (Kansas City has only seven grades below 
the high school.) The average errors per pupil were 8.04 
in the seventh grade, and 6.83 in the first year of high 
school. 

Remedying the situation revealed. When a teacher learns 
the specific language weaknesses of his pupils, he is then in 
position to apply more intelligently his stock of methods and 
devices of instruction. In language, as in the case of the 
other subjects, the teacher must instruct individual pupils 
who are grouped together rather than groups of pupils. 
Furthermore, each pupil should receive the instruction 
which he needs to correct his language errors. 

If pupils are weak in a language ability, such as punctua- 
tion, the laws of habit formation apply. After being sure 
that he understands the function of the punctuation marks, 
a pupil must have practice in punctuating his own writing. 
This probably is not sufficient. Exercises for practice can 
be constructed by taking appropriate material and repro- 
ducing it without the punctuation marks. 



ABILITY IN LANGUAGE AND GRAMMAR 253 

Until a teacher recognizes definite and specific ends to be 
attained, there is certain to be a large degree of dissipation 
of his efforts. Perhaps one reason why language instruction 
so often does not produce satisfactory results is that it is 
not directed toward the engendering of definite abilities. 
That our present standards of language are chaotic is indi- 
cated in the report of a recent investigation. 1 

Present standards for composition indefinite. Six com- 
positions were typewritten without any identifying marks. 
They were "graded" on the scale of 100 per cent by twenty- 
four eighth-grade teachers who were asked to follow certain 
typewritten directions. The six compositions were then 
"completely corrected so far as mechanical or measurable 
errors were concerned." The corrected compositions were 
graded by the same teachers according to the same direc- 
tions. 

If the "mechanical errors" of the compositions were sig- 
nificant factors in determining the first set of marks, the 
second set of marks should be conspicuously higher. How- 
ever, this was not the case. For two of the compositions 
the average "grade" was less after the "mechanical errors" 
had been corrected. The individual marks show that some 
teachers consider form important, and that others tend to 
disregard it in marking a composition. 

Keeping a record of pupils' errors. In teaching spelling, 
teachers have kept a record of pupils' errors and have em- 
phasized these words in their teaching. In our consideration 
of spelling it was urged that teachers first ascertain what 
words their pupils were unable to spell correctly. This plan 
may be adapted to the teaching of other aspects of language. 
The teacher should ascertain the pupils' grammatical errors, 
and then equip them with the rules of grammar which are 

1 Brownell, Baker, "A Test of the Ballou Scale of English Composi- 
tion"; in School and Society, vol. 4, pp. 938-42. 



254 MEASURING THE RESULTS OF TEACHING 

needed to correct them. This has been done on a large scale 
in St. Louis and Kansas City, Missouri. 1 

The point of view in locating errors and applying correc- 
tives is most important. Perhaps the scales and tests de- 
scribed in this chapter will have fulfilled their most impor- 
tant function if they cause teachers to analyze and define 
"language ability" in more specific terms. It is believed 
that their use will tend to produce this result, especially such 
a test as Charters's Diagnostic Test in Language and Gram- 
mar for Pronouns which is based upon an analysis of that 
field. Analysis of "language ability" and specific definition 
of the elements are greatly needed. Upon the accomplish- 
ment of these two things depends the construction of more 
valuable measuring instruments in the language field and 
the scientific determination of methods and devices of 
instruction. 

QUESTIONS AND TOPICS FOR STUDY 

1. Give the copying test to your pupils following the directions care- 
fully. Do the results agree with your estimate of the ability of your 
pupils to copy? 

2. Keep accurate lists of the language errors of your pupils both oral 
and written. What are the rules which are necessary to correct these 
errors? Are they the rules upon which you are placing the most 
emphasis in your teaching? 

3. Do you have definite objective standards of attainment in English 
composition? Can you use the scales described in this chapter to es- 
tablish such standards? 

4. Do you think pupils would be helped by having definite objective 
standards of attainment established for them? 

5. Secure a copy of Willing's Composition Scale and post it in the class- 
room. Have pupils measure their compositions with it. 

6. Why is Charters's Diagnostic Test in Language and Grammar more 
helpful to the teacher than Starch's Punctuation Scale? 

7. What do you think of Charters's method of determining what exer- 
cises to use? Is it a good method? Why? 

1 See report by W. W. Charters in the Sixteenth Yearbook of the National 
Society for the Study of Education, part I. 



CHAPTER X 

THE MEASUREMENT OF ABILITY IN GEOGRAPHY AND 
HISTORY 

Geography and history are different from the school 
subjects treated in the preceding chapters. Subjects such 
as reading, the operations of arithmetic, spelling, and the 
like are sometimes called "tool subjects" to distinguish 
them from such subjects as geography and history which 
are called "content subjects." Silent reading is a tool which 
a pupil uses in studying geography and history. The opera- 
tions of arithmetic are tools which are used in solving 
problems. 

Several tests have been devised for both geography and 
history, and, although they are open to criticism, they are 
more effective as a measuring instrument than tests or ex- 
aminations prepared by the teacher. The questions have 
been very carefully selected, have been evaluated, and the 
tests have been standardized. In both geography and history 
there are a very large number of items of information. Some 
of these are important, while others are unimportant. 
Authorities agree on the importance of some facts; on 
others they disagree. Hence, the selection of the questions 
is very important. On page 10 we found that questions 
were not equally difficult, and hence it is important to have 
the amount of credit to be given for each question scien- 
tifically determined. Finally, pupils' scores cannot be in- 
terpreted without standards. 

The criticism is frequently made, that while it is possible 
to measure "what a pupil remembers," it is not possible to 
measure his ability to answer "thought questions." This 



256 MEASURING THE RESULTS OF TEACHING 

statement is not true. It is possible to measure the ability 
of pupils to think. However, it is very significant that inves- 
tigation has shown that there is a very definite connection 
between a pupil's ability to remember and his ability to 
think. One investigator l in history showed that there was 
a very close agreement between a pupil's score on a memory 
test and his score on a thought test. This result is just what 
we should expect when we recall that reasoning involves the 
use of facts and a person cannot reason effectively unless he 
has command of the necessary facts. The application of 
this relation between ability to remember and ability to 
think is that in using a memory test, we are also indirectly 
measuring the ability of pupils to think in the same field. 
For the most part tests in geography and history have been 
devised so recently that we do not have proof of their value 
as we do in reading and arithmetic. However, certain ones 
of the available tests give promise of being helpful to the 
teacher. In this chapter we will describe two tests in geog- 
raphy and one test in American history. 

I. Geography 

i. Courtis's Standard Tests in Geography for States and 
important cities of the United States. This test is explicitly 
designed to cover only two topics of geography, but all 
teachers will probably agree that they are important ones. 
The plan of the test is to provide each pupil with an outline 
map of the United States showing the boundaries of the 
several States. Each State is given a number. The first 
part of the test consists of answering for each State the 
question, "On, the map above what is the number of 
? " In the second part of the test the pupil is 

1 Buckingham, B. R., "Correlation between Ability to Think and Abil- 
ity to Remember, with Special Reference to United States History"; 
in School and Society (April 14, 1917), vol. 5, p. 443. 



ABILITY IN GEOGRAPHY AND HISTORY 257 

asked to give the number of the State in which certain cities 
are located. The preliminary test which is given, so that 
the pupil may understand just what he is to do, is repro- 
duced in Fig. 40, to illustrate this type of test. 



INSTRUCTIONS 

Write after each state the 
number printed in that state, 
on the map at the right. For 
instance: Write 1 after Mich- 
igan. What number should 
be written after Ohio? 

In the same way, after each 
city write the number of the 
state in which that city is 
located. Write 1 after De- 
troit. What should be writ- 
ten after Chicago? 




STATE 



CITY 



Questions 



1. Michigan?.. 

2. Ohio? 

3. Indiana ? . . . 

4. Illinois?.... 

5. Wisconsin?. 



Number 



Questions 



1. Detroit? 

2. Chicago? 

3. Cleveland? .... 

4. IndianapoUs ?. 

5. Madison? 



Number 



Fig. 40. Illustrating Courtis's Standard Test in Geography for 
States and Important Cities of the United States 



258 MEASURING THE RESULTS OF TEACHING 

Marking the test papers and recording the scores. De- 
tailed directions for marking the test papers and for record- 
ing the scores are furnished with the test and hence need not 
be given here. 

2. Hahn-Lackey Geography Scale. A different type of 
test has been devised by H. H. Hahn and E. H. Lackey. 
This scale consists of questions which were very carefully 
selected. The plan of selection is described as follows i 1 

Since texts will be used by a large majority of teachers for years 
to come, our primary purpose was to construct a scale for the test- 
ing of the teaching of geography from text-books. But when we 
realized that not one but a number of texts are being taught, we 
had to modify our plan. Our first modification consisted of limit- 
ing our questions to the phases of geography treated in common 
by six modern texts. Then we found that some of these phases 
were treated more fully by some authors than they were by others. 
A second modification of our plan was, therefore, necessary; 
namely, to select the common subject-matter, or, in other words, 
the esentials of subject-matter in each phase. In the selection of 
the essentials of subject-matter, the common subject-matter in 
these texts was largely our guide, but we also checked our exer- 
cises by principles and minimum essentials as they have been 
worked out by makers of geography curricula. (See 1914 and 1916 
Yearbook [of the National Society for the Study of Educationl.) 
Over six hundred questions and exercises were selected by three 
teachers, covering this common subject-matter. These exercises 
were then examined by the authors of the scale, first, with refer- 
ence to repetitions, and duplications were eliminated. They were 
next examined for language difficulty. The wording of many of 
the exercises was changed, some of them were actually tried out on 
children, and in many instances technical expressions which would 
convey exact meaning to mature students of geography were elimi- 
nated and the ordinary language of children substituted. This is 
particularly true of the exercises in the lower reaches of the scale. 
The exercises intended for the upper reaches of the scale were not 
freed from technical expressions the meaning of which pupils are 

1 From an unpublished account of the derivation of the scale by the 
authors. 



ABILITY IN GEOGRAPHY AND HISTORY 259 

expected to know as evidence of geography ability. Thus we find 
such expressions in the scale as "the Fall Line," "climate," 
"continent," "natural wonders," "natural geographic barriers," 
"agencies," "cyclonic storms," and many others equally as tech- 
nical. The exercises were examined, in the third place, as to their 
scope, as suggested before. Nothing was included beyond the 
essentials of geography. Finally, the list of exercises was revised 
so that it contained about an equal number of memory and thought 
questions. 

These questions were classified according to difficulty by 
giving them to 1696 pupils in twelve schools in two States. 
A section of the scale is reproduced in Fig. 41. The num- 
bers at the top of the columns represent the per cent of 
correct answers which were given by the 1696 pupils. These 
per cents are tentative standards. 

Using the scale. This geography scale is a classified list 
of questions from which the teacher can select questions 
for a test. Since the questions in any column are equally 
difficult, it is best to take the questions for a test from one 
column. These may be given in the usual way by writing 
them on the board. It is better if each pupil is provided 
with a mimeographed copy with space left for writing in 
the answers. The teacher should not explain the meaning 
of any words used in the questions because the results will 
then not be comparable with the standards. Ten questions 
will make a test of convenient length and probably is the 
best number to use. 

Scoring the papers. When ten questions are used and all 
have been chosen from the same column, each one may be 
considered to have a value of 10 credits. This will make 
the total number of credits 100. For scoring the papers the 
authors have prepared a score card. The portion of it which 
applies to the section of the scale reproduced in Fig. 41, is 
given below. These directions must be followed if the result- 
ing scores are compared with the standards. The score of a 



260 MEASURING THE RESULTS OF TEACHING 

pupil is the sum of the credits which he earns on the list 
of questions. The class score is the average of the scores 
of the members of the class. 

What to accept and what to reject in scoring answers. 
Many of the exercises in the Hahn-Lackey Geography Scale 
admit of only one answer; but the scale contains exercises 
to which the answers may vary. In order that the scoring 
of the answers by teachers of different localities may be 
uniform and the scores be comparable with those of the 
scale, the authors have prepared a list of typical an- 
swers they accepted and typical answers they rejected in 
making the scale. In this list the answers to the exercises 
are given in the order in which they occur in the position 
of the scale reproduced in Fig. 41. 

"F" means full credit; "P" means part credit; "N" means no 

credit. 
42. Different kinds of meat was credited as only one kind of 
food. 
1. F. "Brazil"; "South America"; "Mexico"; "Central 
America." 

103. F. "Rays fall more vertical"; "Farther south"; "Nearer the 

equator." 
N. "Ocean breezes"; "Gulf Stream." 

104. F. "Capacity for water"; "Can go a long time without a drink." 
18. F. "Let it down in the valleys or sea"; "Leave it on the 

bank"; "Form Islands"; "Drop it at the mouth"; "Drop 
it when the current is not swift." (Any answer that indi- 
cates that rivers take soil from one place and put it in 
another place.) 

29. F. Any two lines of work; as, "Plants grain and harvests it"; 
"Raising cattle and farming"; "Raises crops and milks"; 
"Farming and selling things." 
P. One half credit for only one line of work. 

98. F. "No food for horses"; "Too cold for horses." 
6. F. "Earth" "Land" "Rock" "Stone" "Mountains"; 
"Sand"; "Plains"; "Plateaus." (Any answer indicating 
a knowledge of the bed of the ocean.) 






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ABILITY IN GEOGRAPHY AND HISTORY 261 

19. F. "Out of the ground"; "From veins"; "Springs"; "From 
little streams in under the ground"; "From moisture in 
the ground." (Any answer clearly implying underground 
source.) 

23. F. Any two. "Bring rain"; "Turn mills"; "Fresh air"; 
" Makes temperature equal"; "Makes pressure equal"; 
"Scatters seeds"; "Causes ocean currents." 

68. F. "Good harbors"; "Commerce"; "Importing and export- 
ing goods"; "Trade carried on there." 

47. F. Any two. "By railroad"; "Wagon"; "Mail"; "Ships." 

48. F. Any two. "Railroad bridge"; "Boat"; "Wagon bridge"; 

"Fording." 

57. F. Any two. "Fish"; "Navigation"; "Sport"; "Water- 
power"; "Drains the land." 

39. F. Any answer indicating a knowledge of the ocean as a 
source of vapor in the air; as, "Fills the air with vapor"; 
*' Makes air moist." 

21. F. "Winds"; "Breezes"; "Air"; "Atmosphere." 

Interpreting the scores. Two things must be kept in 
mind if a satisfactory interpretation of the scores is obtained: 
(1) The standards given at the head of the columns do not 
represent the exact per cent of correct answers obtained. 
For example, 50, the fourth grade standard for column R, 
represents values from 46.8 to 53.2. Thus, small differences 
between scores and standards are not significant. (£) The 
standards are given in terms of a scale of 100 units or a per 
cent scale. It is also customary to use a per cent scale for 
reporting "school grades," or at least for defining them. 
Some per cent, as "60," "70," or "75," is chosen as the 
"passing mark." A score of 79 on a set of questions chosen 
from column S of this scale does not mean "79 per cent" as 
a school mark. This score of 79 is above standard in the 
fourth and fifth grades. It is just standard in the sixth 
grade and below standard in the seventh and eighth grades. 

When a pupil has a score which is just standard, he is just 
an average pupil because the standard is an average score. 



262 MEASURING THE RESULTS OF TEACHING 

If five marks, such as A, B, C, D, and E (A being the high- 
est mark), are used, such a pupil would be given a mark of C. 
If "grades" are reported in per cents and 75 is the passing 
mark, a score of 79 when the standard is 79 should be trans- 
lated as about "85 per cent." Scores above and below 
standard should be interpreted with the standard repre- 
senting the average. 

II. American History 

Harlan's Test of Information in American History. The 
items of information called for by this test are found in 
practically all American history textbooks, being based on 
the study by Bagley and Rugg of twenty-three textbooks 
to determine the content of American history. 1 This in- 
sures the questions being well selected. The credit to be 
given for answering each question has been determined and 
a score card is furnished with the test so that the marking 
of test papers may be uniform. The test consists of ten 
exercises. The first, fourth, and ninth are reproduced to 
illustrate their nature. 

Exercise I 

At the right of the page are the names of some men mentioned 
in American history. Fill in blanks with the names which properly 
belong there. 

1. America was discovered by 

Score near the close of the fifteenth century Jefferson 

2. The name of the man who is supposed to Cornwallis 
have discovered the Pacific Ocean is William Penn 

3. The first President of the United States was Lafayette 
Patrick Henry 



1 Bagley, W. C, and Rugg, H. O., The Content of American History as 
Taught in the Seventh and Eighth Grades. (University of Illinois, School of 
Education, Bulletin no. 16, 1916.) 



ABILITY IN GEOGRAPHY AND HISTORY 2G3 

4 is the name of a dis- Columbus 

tinguished Frenchman who aided the col- Benj. Franklin 

onists in securing their independence Washington 

5 surrendered to the John Cabot 

colonial troops at Yorktown Balboa 

Exercise IV 

Tell the very first thing you would do under each of the following 
conditions; also what you would do next: 

1. If a neighbor were to present to you for your signature a 
Score petition to have some man removed from public office, — 

What would you do first? 

Would you sign the petition? 

2. If a man imprisoned in the county jail for some serious crime 
should be taken out by a mob with the intention of hanging 
him, — 

What ought to be done first? 

Then what? 

Exercise IX 

The following topics represent matters of importance in the his- 
tory of the United States. State definitely of what significance 
each has been. 

1. Articles of Confederation 

Score 

2. Mason and Dixon's line 

3. Monroe Doctrine 

4. The Tariff 



Standards. The total amount of credit allowed for the 
ten exercises is 100. Over two thousand pupils in the seventh 
and eighth grades have been tested at the end of the respec- 
tive years. The median scores are: Seventh grade, 56; 
eighth grade, 86. 



264 MEASURING THE RESULTS OF TEACHING 

As in the case of geography, these standard scores are the 
scores which should be made by the average or median 
(middle) pupils. Consequently, when translating these 
scores into school marks, a score which is standard should 
be given the "school grade" which represents the average 
pupil. 

Diagnostic value of the test. The different exercises call 
for different types of information: dates, names, causes, 
meanings of historical terms, etc. By tabulating the credits 
earned on the different exercises in the way given for Char- 
ters^ Diagnostic Tests in Language and Grammar (Fig. 39), 
a teacher may learn which phases of history need additional 
emphasis. 

Other tests in geography and American history. Since 
tests in these two fields have been devised only recently and 
have not been used sufficiently to determine which ones are 
most helpful to the teacher we list here other tests. Informa- 
tion concerning them may be obtained by consulting the 
reference given or by writing to the address. 

Geography 

1. The Boston Tests. The two tests of this series — one 
on the United States and the other on Europe — consist of 
well-chosen questions. The relative difficulty of the ques- 
tions was determined upon the basis of the per cent of cor- 
rect answers. The tests were devised in an effort to deter- 
mine (1) the character of achievement in geography, and 
{%) the possibility of scientific measurement of educational 
results in geography. This significant comment is made: 
"The results show how inadequate the customary examina- 
tion or test in geography is to measure ability in geography." l 

1 Geography ; A Report on a Preliminary Attempt to Measure Some Edu- 
cational Results. (Boston, Department of Educational Investigation and 
Measurement, Bulletin no. 5, School Document no. 14, 1915; p. 38.) 



ABILITY IN GEOGRAPHY AND HISTORY 265 

2. Buckingham's Geography Test. This test was devised 
for use in the survey of the Gary and Prevocational Schools 
of New York City. It consists of two sets of twenty ques- 
tions which were evaluated upon the basis of the per cent 
of correct responses. 1 

3. Starch's Geography Tests, Series A. The common ele- 
ments of five geography texts have been arranged in five 
parallel tests. The exercises of the tests are in the form of 
mutilated sentences. 2 

4- William's Standard Geography Tests. These are a series 
of tests arranged to test quickly and easily the pupil's knowl- 
edge of certain geographical facts. The facts for the tests 
on the world are grouped under these heads: (1) geograph- 
ical divisions, (2) form and motion of the earth, (3) the 
hemispheres, (4) land and water forms, (5) homes of the 
races, (6) industries, and (7) largest cities. 3 

5. Branom and Reavis Completion Test for the Measure- 
ment of Minimal Geographic Knoidedge of Elementary School- 
Children. This test was very carefully constructed and ap- 
pears to have a high degree of merit. No standards have been 
published. 4 

History 

1. Buckingham's Tests. These tests were used in the sur- 
vey of the Gary and Prevocational Schools of New Y T ork 
City. They consist of two sets of questions which have been 
evaluated on the basis of the per cent of correct answers. 

1 Seventeenth Annual Report of the City Superintendent of Schools. (New 
York City, 1914-15.) 

2 Address Daniel Starch, University of Wisconsin, Madison, Wisconsin. 

3 Witham, E. C, "A Minimum Standard for Measuring Geography"; 
in American School Board Journal (January, 1915), vol. I, pp. 13-14. 
Address E. C. Witham, Southington, Conn. 

4 Seventeenth Yearbook of the National Society for the Study of Education, 
part i, pp. 27-39. (Public School Publishing Company, Bloomington, 
Illinois, 1918.) 



266 MEASURING THE RESULTS OF TEACHING 

More recently Buckingham has studied the relation between 
the ability to remember historical facts and the ability to 
use them. In this study specially devised tests were used. 1 

2. The Bell and McCollum Test This test consists of a 
series of questions which have been very carefully selected 
because of their importance. The topics included are: 
(1) dates-events, (2) men-events, (3) events-men, (4) his- 
toric terms, (5) political parties, (6) divisions of history, 
and (7) map-study. The test can be administered in a forty- 
minute period. 2 

3. Starch's American History Tests, Series A. This test 
is based upon the facts and principles common to five mod- 
ern texts. The exercises are in the form of mutilated sen- 
tences. Four duplicate forms are available. 3 

QUESTIONS AND TOPICS FOR STUDY 

1. What do you think of the method used in selecting the questions for 
the Hahn-Lackey Geography Scale? Is it a good method? Why? 

2. Can we determine what pupils should know by examining textbooks? 
Why? In such a subject as geography, how can you determine what 
pupils should know? 

3. What is a " tool subject " ? A " content subject " ? 

4. How is a score on the Hahn-Lackey Geography Scale to be inter- 
preted? 

5. Select ten questions from the Hahn-Lackey Geography Scale. In 
what ways do they form a better test than a list of questions you 
might prepare? 

6. How was Harlan's American History Test made? What are its 
strong points? Compare it with the usual history examination. 

1 Seventeenth Annual Report of the City Superintendent of Schools. (New 
York City, 1914-15.) 

2 Bell, J. C, and McCollum, D. F., "A Study of the Attainments of 
Pupils in United States History"; in Journal of Educational Psychology 
(May, 1917), vol. 8, pp. 257-74. 

3 Address Daniel Starch, University of Wisconsin, Madison, Wisconsin. 



CHAPTER XI 

EDUCATIONAL MEASUREMENTS AND THE TEACHER 

In Chapter I evidence was presented which showed that 
measurements of the results of teaching, both by teachers* 
estimates and by examinations, were strikingly inaccurate. 
More accurate measurements of the results of teaching can 
be secured in two ways: (1) By using standardized tests. 
A number of these instruments have been described in the 
preceding chapters and the teacher has been told how to 
make the greatest use of the information obtained. (2) By 
introducing certain improvements into the making and 
using of examinations set by the teacher. Before presenting 
suggestions for making these improvements, it may be 
helpful to consider a question which may have occurred to 
some readers : What is the value of measuring accurately the 
results of teaching? The answer to this question will be pre- 
sented under two heads: (1) A common-sense answer, or 
logical reasons; (2) experimental evidence. 

(i) Logical reasons for the value of accurate measure- 
ments by means of standardized tests. It is a generally 
accepted principle that in any field of human endeavor the 
most efficient results are attained when one has a definite 
aim to work for and instruments for determining from 
time to time how much has been accomplished. A definite 
aim makes it possible for the worker to direct his efforts 
toward the particular things to be accomplished, instead 
of scattering them over an indefinite field. Instruments 
for measuring results make it possible for the worker to 
know what he has accomplished and where he needs to 
place greater effort and where less effort. It is also possible 



268 MEASURING THE RESULTS OF TEACHING 

for him to learn whether the materials and methods he is 
using are effective and which materials and methods are 
most effective. 

This principle is the foundation of success in the busi- 
ness world. The merchant, manufacturer, or farmer who 
does not have a definite aim and who does not measure 
his accomplishment from time to time is most frequently 
a failure. Bankers measure the results of their business 
every day. Merchants take inventories once a year and in 
many cases more frequently, sometimes a partial inventory 
every day. They consider this procedure necessary for 
success. 

The teacher is a manufacturer. His raw material is the 
children. Textbooks, school buildings, equipment, libraries, 
and methods and devices of teaching are the " machines " 
or instruments which he uses to change this raw material 
into the finished product or educated boys and girls who 
are prepared to do their part in the life of the community, 
State, and Nation. Without definite aims the teacher cannot 
plan his work effectively. He does not know, except in an 
indefinite or general way, what he is to do. If he has definite 
aims, but no instruments for measuring his results accu- 
rately, he cannot learn when he has attained his aims. Thus 
he is compelled to work in the dark. If he makes inaccurate 
measurements, but considers them accurate, he is in a still 
more serious situation. His efforts are almost certain to be 
expended unwisely. 

Evidences of the lack of definite aims. It may appear to 
some teachers that the aims for the several grades as stated 
in courses of study are sufficiently definite. In the case of 
reading it was pointed out on pages 82-85, that oral read- 
ing was sometimes over-emphasized, while silent reading 
was neglected, and that in certain cases the rate of silent 
reading was not sufficiently emphasized. In the operations 



MEASUREMENTS AND THE TEACHER 209 

of arithmetic the rate of work is sometimes neglected (see 
pages 23 and 25). Cases of irregular progress are shown in 
Figs. 119 and 122. When classes make irregular progress in 
ability to do the different types of examples, as is shown 
in these figures, the lack of definite aims is a contributing 
cause. 

Another type of evidence is given in Fig. 42. 1 This figure 
is drawn by the method given on page 110, and shows five 
sets of median scores for rate and accuracy in Addition 
(Series B) in Grades four to eight: (1) Courtis Medians, 
(2) Medians for Cuyahoga County (Ohio), (3) Brook Park, 
(4) Rocky River, and (5) Shaker Heights. (The last three 
are three district schools in Cuyahoga County.) The broken 

line ( ) connecting the small circles representing the 

Courtis Medians shows gradual and regular progress from 
grade to grade. The same condition is exhibited for Cuya- 
hoga County as a whole, but a distinctly different situation 
is shown for the three schools. In the fourth grade the 
Brook Park School is very low in accuracy. The fifth-grade 
pupils show a decided gain in accuracy, but almost no prog- 
ress in rate of work, while the accuracy median for the 
sixth grade is below that for the fifth grade. The rate of 
work for these three grades is approximately the same. 
From the sixth grade to the seventh marked progress in 
both rate and accuracy are shown and from the seventh to 
the eighth grade the progress is almost wholly in accuracy. 
A study of the lines representing the median scores of Rocky 
River and Shaker Heights reveals similar irregularities in 
the progress from grade to grade. This condition is prob- 
ably due in a large degree to the fact that the teachers did 
not have definite aims for the several grades and had not 

1 This figure is taken from the Third Annual Bulletin and School Direc- 
tory of Cuyahoga County (Ohio) School District, p. 71, by County Superin- 
tendent A. G. Yawberg. 



270 MEASURING THE RESULTS OF TEACHING 




Fig. 42. Medians in Speed and Accuracy in Addition Test, Series B, 
for Pupils op Grades 4 to 8 inclusive, showing Courtis's Me- 
dians, Medians for Cuyahoga County, and for Three Districts in 
the County. Rate on Vertical Scale, Accuracy on Horizontal 
Scale. 

measured the results of their instruction to learn to what 
extent these aims were being realized. 

Courses of study do not give definite working specifica- 
tions for teachers. Our present courses of study represent 
the efforts of those occupying supervisory positions in our 
school systems to provide teachers with specifications for 
their work. How well they have succeeded is illustrated by 
the following quotations from typical courses of study : 



MEASUREMENTS AND THE TEACHER 271 

Fourth Grade 

Reading and Literature. Stories read and told to the elass; 
Roman stories, American history stories relating to geography, 
selections from Greek and Teutonic mythology, and poems. 

A few choice selections of appropriate prose and poetry are to 
be studied, committed to memory, and recited or dramatized. See 
that the pupil stands on both feet and reads smoothly and confi- 
dently. Watch the voice of pupils; use breathing exercises; and 
avoid harsh, strained reading. Have pupils read many selections 
silently, then reproduce the thought aloud in order to develop the 
power of gaining and expressing the thought of the text. Aim to 
enlarge the pupil's vocabulary, to help him master the thought 
content, and gain the power to read in a pleasing, well-modulated 
tone. Use much supplemental reading. Explain the purpose of 
the children's department in the Public Library, and encourage 
pupils to read books therefrom. 

Following these general directions, the selections to be 
read are specified: 

Third Grade : B Class 

Handwriting. Daily drill, lessons five, six, or seven. 1 During 
the entire year these drills should be used for a few moments at 
the beginning of each writing lesson. 

Beginning with lesson five, take the lessons in consecutive order 
to lesson thirty-five. 

After developing a letter with the class take, from the writing 
book, a word beginning with the same letter and use it for practice. 

If the letter is a capital, follow the word practice by using a 
sentence beginning with this letter. All words and sentences should 
be taken from the writing book. 

Grade J+B. Arithmetic 

Leading topics. The four fundamental processes with emphasis 
upon multiplication. 

Review. Regularly, constantly, and from the first. The addition 
combinations, subtraction, reading and writing numbers, simple 
fractions. 

1 Reference to a Manual for Teachers, used in this school system. 



272 MEASURING THE RESULTS OF TEACHING 

Multiplication. The tables completed and made automatic. 
Problems with two-place multipliers. Rapid oral practice. 

Division. Short division with long division brace. Rapid oral 
practice. 

Fractions. Simple fractions and mixed numbers as needed in 
actual practice on concrete form problems. Largely oral and 
objective. 

Concrete problems. One-step problems. 

Applied problems. Farm products, farm marketing, farm profits. 

Measures. Quart, gallon, peck, bushel, pound, ton, cord, etc., 
as required by applied problems. 

In the fourth-grade course of study for reading, nothing 
is said about the rate at which a pupil is expected to read 
orally or the rate and degree of comprehension of silent 
reading. The teacher is told to "enlarge the pupils' vocabu- 
lary," but he is not told how much to enlarge it. In hand- 
writing nothing is said about the rate or quality of writing. 
In arithmetic the multiplication tables are to be "completed 
and made automatic." This is indefinite because there are 
many degrees of automatization. What one teacher would 
call automatic, another would not. " Rapid oral practice " 
is likewise indefinite. 

Definite specifications for these subjects could be given 
by stating the rate and quality of work expected of the 
pupils. For example, in handwriting the teacher would have 
a definite aim if he was told that fourth-grade pupils should 
be able to write memorized material at the rate of 56 letters 
per minute and with a quality of 50 as measured on the 
Ayres Scale. In arithmetic the aim would be definite if he 
were told that fourth-grade pupils should be able to write 
the answers to the multiplication combinations at the rate 
of 23 per minute. When the teacher has his aims expressed 
in this definite way, he still needs to measure results to learn 
to what extent he is realizing his aim. 

(2) Experimental evidence of the value of standardized 



MEASUREMENTS AND THE TEACHER 



273 



tests to the teacher. Several instances of the value of stand- 
ardized tests have been given in the preceding chapters. 
For reading, see pages 73 to 89; for arithmetic, see page 
151; additional evidence is given in Figs. 43, 44, and 45. 
In Fig. 43 a sixth-grade teacher in a small town gave 



ffuMraotlon 
At Rt 



KUltiplioatloa 
At Bt 



Dlrl.Blon 

At at 




Fig 43. Showing the Median Scores op a Sixth-Grade Class in 
September, 1917, and in April, 1918, as measured by the Courtis 
Standard Research Tests in Arithmetic, Series B 

Dotted line September medians. Solid line (upper) April medians. Heavy solid line, 
standard median scores. 



the Courtis Arithmetic Tests, Series B, in September, 
1917. The condition revealed is shown by the lower line 
in the figure. The standards or the definite aims to be 
attained are represented by the heavy solid line. The re- 
sults of the teacher's efforts are shown by the upper line 
which represents the median scores for April, 1918. This 
teacher knew what her pupils could do at the beginning 



274 MEASURING THE RESULTS OF TEACHING 

of the year and the standards which were to be attained. 
She had the satisfaction of knowing that these had been 
attained. 

In Cleveland, Ohio, spelling was tested in May, 1915. It 
was again tested in May, 1917. In Fig. 44 the "efficiency" 
of spelling in certain of the buildings is showing for these 
two tests. The broken line represents the "efficiency" 1 for 
the test in May, 1915. The solid line represents the "effi- 
ciency" for the test in May, 1917. The significant thing in 
this illustration is the material improvement in spelling 
"efficiency" of those buildings which had low average scores 
in 1915. This suggests that when a teacher knows that he is 
not securing standard results, he is likely to increase the 
effectiveness of his instruction. 

In the city of Boston standardized tests in arithmetic 
were given in 1912 in twenty-nine schools and have been 
given at least once each year since. In Fig. 45 these are 
called Group A Schools. In the Group B Schools the stand- 
ardized tests in arithmetic were given first in 1913 or 1914. 
Group C includes those schools in which the results of in- 
struction in arithmetic were measured for the first time in 
1915. Group A represents 18,391 pupils, Group B, 15,241 
pupils, and Group C, 11,836 pupils. In May, 1915, standard- 
ized tests in arithmetic (the Courtis, Series B) had been 
used in Group A for three consecutive years, in Group B 
for one or two years, and in Group C they were being given 
for the first time. 

We have here, therefore, an opportunity to study the 
effect of using such tests. If the tests are helpful to the 
teacher, those schools in which they have been used for three 

1 "Efficiency" means here the quotient of the average score divided by 
the standard given by Ayres on his Spelling Scale. Since these standards 
are lower than the average scores in certain cases those quotients are 
above 100. 




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276 MEASURING THE RESULTS OF TEACHING 

years should show the best results and those in which they 
have been used for one or two years should stand above 
those in which they were given for the first time. Fig. 45 

Kumber of examples attempted 

2 4 6 8 10 12 14 16 

'■' i »' " ■■> » ■ I. « i ■ 

Addition 



Group 

B| 

CI 



Subtraction 



Multiplication 



Division 



Fig. 45. Showing Effect of Continuous Use of Courtis's Standard 
Research Tests, Series B, in Boston, Eighth Grade, 1915 

Group A schools continuous use for three years. Group B schools use for one to two years. 
Group C schools not given until this record was secured. (After Ballou.) 

represents the median number of examples attempted by 
the eighth-grade pupils in each of the three groups of schools. 
In every case the Group A Schools have the highest medians 
and the Group B Schools stand above those of Group C. 
The median scores for accuracy are not represented, but 
they show the same condition. Thus, this figure shows that 



MEASUREMENTS AND THE TEACHER 277 

in the case of the eighth grade superior results in the opera- 
tions of arithmetic are attained by those schools in which 
standardized tests are used. The results for the other grades 
in Boston are not so striking, but they furnish additional 
evidence that it is helpful to measure the results of instruc- 
tion accurately. 

Making examinations yield more accurate measurements. 
In Chapter I the following criticisms were made of the 
measurement of the results of teaching by examinations: 
(1) The questions cover a wide range of topics making the 
"grade" have no definite meaning. (2) The questions are 
generally not equally difficult and the same amount of credit 
should not be given for answering different questions. The 
judgment of a teacher in regard to the amount of credit 
which should be given for answering a question correctly is 
not reliable. (3) Teachers do not mark examination papers 
accurately. (4) The pupil's rate of work is usually neglected 
even in those subjects where it is important. (5) Standards 
are not available for interpreting the measures. 

It is not possible for the teacher to eliminate entirely the 
defects enumerated by these criticisms, but it is possible 
for him to reduce them. Greater care in choosing and fram- 
ing the questions will materially reduce the first defect men- 
tioned above. Catch questions should always be avoided. 
Also the question should be stated so that the pupil will 
understand what is called for. The questions should be 
important. Unimportant facts should not be called for unless 
there is some particular reason for doing so. 

The amount of credit to be given for answering a question 
correctly cannot be accurately determined, but a helpful 
rule to follow for questions which are approximately equal 
in importance is that the most credit should be given for the 
most difficult question and the least credit for the easiest. 

Both of the above suggestions will tend to increase the 



278 MEASURING THE RESULTS OF TEACHING 

accuracy of the marking of examination papers. In addition 
a systematic plan will materially reduce this source of error. 
Kelly 1 describes the following experiment: Six fifth-grade 
teachers gave a uniform examination in arithmetic to their 
pupils. Each teacher marked the papers for her own pupils, 
but did not record the marks on the papers. The superin- 
tendent asked a teacher, who was unusually systematic in 
marking examination papers, to prepare a definite plan for 
marking these papers. After she had done so, she marked 
all of the papers in accordance with this plan. Then the 
teachers who had first marked the papers marked them a 
second time following her plan. This provided two marks 
for each paper by the classroom teacher, the first without 
following a systematic plan, and the second using a definite 
plan. Each of these marks was compared with the mark 
of the teacher who marked all of the papers. In Table XXIV 
the six teachers are designated by the letters A, B, C, D, E, 
and F. The table is read as follows: When no systematic 
plan was followed, teacher A marked one paper 16 to 20 
points lower than the "judge," one paper 7 points lower, two 
papers 4 points lower, two papers 2 points lower, agreed 
with the "judge" on one paper, etc. The differences be- 
tween the marks given when the classroom teachers had no 
systematic plan and when they followed such a plan are 
very striking. In the first instance the marks assigned by 
the teachers agreed with those assigned by the "judge" in 
only 5.5 per cent of the cases, while in the second instance 
they agreed in 63.5 per cent of the cases. Thus the ex- 
periment shows that with a systematic plan for marking 
papers, the marks will be more accurate. 

The rate at which the pupil works can easily be measured 
in such subjects as reading, handwriting, and the operations 
of arithmetic. It is only necessary to place a time limit 
1 Kelly, F. J., Teachers Marks, p. 84. 



MEASUREMENTS AND THE TEACHER 



279 



upon the examination such that no pupil will answer all of 
the questions. The number of questions answered will be 
a crude measure of his rate of work. 



Table XXIV. Distributions of Differences between Two 
Sets of Teachers' Marks on Fifth-Grade Arithmetic 
Papers — First, without any Effort to unify the 
Methods used, and Second, by a Common Standard 
(after Kelly) 



Range of 


Without standard 


With standard 


Difference* 


A 


B 


C 


D 


E 


F 


Total 


A 


B 


C 


D 


£,' 


F 


Total 


21 or more 

16 to 20 


i 

*2 
2 

1 

2 
6 
9 
5 
2 
1 

i 

i 

i 


"\ 

"\ 
2 
1 
2 

4 
2 
5 

4 

5 

1 

i 

3 
1 
1 
2 

i 

2 


2 
2 
2 

1 
4 

4 

3 

2 
4 
2 


1 

'i 

l 

l 

3 

1 

2 
2 

i 

2 

3 

6 
2 
2 

1 

i 

i 
a 


o 

1 

i 
l 
l 

2 

3 

1 
1 
1 
1 

1 

2 

1 

2 
3 
2 
5 


1 

1 

2 

2 
1 

1 
1 
1 
1 
2 
2 
2 

4 

1 

1 

1 

i 

'i 

i 
l 


2 

3 
2 

1 
3 
2 
4 
1 
4 
5 
5 
4 
7 

10 

11 

8 

18 

12 

14 

16 
13 
17 
10 

9 
6 
4 
3 

2 
3 
3 

1 
2 
o 

5 


i 
'4 

2 
22 

5 

1 


i 
i 

3 

30 

i 

2 
2 

1 


i 

i 

l 

4 
16 

2 

3 
2 

3 

1 
1 


i 
i 

3 
5 

16 

2 

i 

3 
2 

1 

i 


i 

7 
1 

29 

1 


i 

1 

26 
3 

i 




15 

14 

13 

12 

11 

10 

9 

8 

7 


i 
i 

i 


6 

5 

4 


*2 


3 

2 

1 




3 

17 
16 

139 


1 


13 


2 


5 


3 


6 


4 


8 


5 


4 


6 


2 


7.. 

8 

9 


•*• 


10 




11 

12 




13 

14 

15 

16 to 20 

21 or more 


i 


Totals 

Medians. 


35 
+3 


41 



35 

+1 


36 
+6 


39 
— 1 


33 

—4 


219 
+1 


35 


41 


35 


36 


39 


33 


219 



230 MEASURING THE RESULTS OF TEACHING 

The lack of standards can be partially remedied by having 
other teachers give the same examination to other pupils 
of the same grade. Where this is not possible, the teacher 
should verify what he considers a satisfactory standard by 
using standardized tests occasionally. If the standardized 
tests show a class to be near the standard, the teacher may 
conclude that his standard is satisfactory. If the work of the 
class is shown to be unsatisfactory then the teacher should 
conclude that his standards are too low unless her examina- 
tions have also shown the class to be doing a low grade of 
work. 

QUESTIONS AND TOPICS FOR STUDY 

1. How may examinations be made more accurate measuring instru- 
ments? 

2. Do you think that examinations have functions other than that of 
measuring the abilities of pupils? If so, what are they? 

3. Repeat the experiment described on page 218 and compare your re- 
sults with those given in Table XXIV. 

4. Why is a general aim not sufficient? 

5. What are the objections to our present courses of study with respect 
to the statement of aim? 

C. How can standardized tests be used in setting the aim for the teacher? 

7. Criticize your course of study. How could you make use of standard- 
ized tests in improving it? 

8. Why should teachers use standardized tests? (Give all of the reasons 
you can think of.) Do they require more time on the part of the 
teacher than similar tests he might prepare? 



CHAPTER XII 

SUMMARY 

The use of standardized tests by teachers may be sum- 
marized under the following steps. 

i. Selection of a test to use. For the most part teachers 
should accept the advice of experts in selecting a test. How- 
ever, it is well for teachers to ask these questions about a 
test: (1) Has it been widely used or is it likely to'be widely 
used in the near future? (2) How much time is required to 
give the test, to mark the papers, and to record the scores? 
These points are very important. If the test has not been 
widely used or there is no prospect of its wide use in the near 
future, reliable standards will not be available. Also the 
general use of a test indicates that it has been found helpful 
to teachers. If a test requires a large expenditure of time, a 
teacher is not likely to receive adequate returns for the time 
spent. In general a teacher should choose a test which is 
simple to use and which requires only a moderate amount 
of time. 

2. Giving the test. In giving a test to a class the teacher 
should follow the directions. If this is not done, compari- 
sons of the resulting scores with the standards will not be 
valid. Also the teacher should bear in mind that his purpose 
should not be to secure as high scores as possible, but to 
secure a true measure of the abilities of his pupils. In order 
to do this the pupils must not be excited or urged to work in 
an unnatural way. 

The manner in which the test is presented to the pupils 
affects the scores. The purpose of measurement is defeated 
if the test is presented to the pupils in such a way that their 



282 MEASURING THE RESULTS OF TEACHING 

response is unnatural. For example, in handwriting, if the 
pupils write at an unnatural rate the quality of their hand- 
writing will be affected. 

3. Marking the test papers. Explicit directions and score 
cards are generally provided for doing this. Here also the 
teacher must follow the directions. If he does not, a valid 
comparison cannot be made with the standards. In the case 
of a few tests, the papers are marked by the pupils as the 
teacher reads the correct answers. This can be done in the 
case of tests in the operations of arithmetic, in certain read- 
ing tests, and in spelling. Courtis advises that this plan be 
followed in order to save time which may be used in the 
interpretation of scores. In the case of handwriting and 
composition, the teacher should equip himself for accurate 
rating of papers by systematic training. 

4. Recording the scores and calculating class scores. 
Blanks for recording the scores are usually furnished with 
the tests. When they are at hand, this step is very simple 
after the teacher has had a little practice. 

5. The interpretation of scores. In interpreting both in- 
dividual and class scores, standards are necessary. Many 
people understand facts more easily when they are repre- 
sented graphically. Hence, it is well to employ some means 
of graphical representation. 

6. Correction of the defects revealed by the test. The 
correction of the defects revealed by the test is the culmina- 
tion of the preceding steps. It is in this step that the value 
of standardized tests is realized. Without this step standard- 
ized tests become mere "playthings" and their use cannot 
be justified. The situation created is similar to that which 
would exist if a physician examined a patient carefully and 
determined the nature of his ailment, but did not prescribe 
any remedial treatment. In our zeal to convert teachers to 
the acceptance of the principle that the measurement of 



SUMMARY 283 

certain results of instruction is possible, there has been a 
tendency to overlook this step. In fact some have even sai< 1 
that they were content to apply the tests and reveal to the 
teachers the shortcomings of their work. These persons 
would leave to the teachers the difficult problem of remedy- 
ing the defects. As a result not a few teachers have failed 
to see in the tests anything more than a new "plaything," 
which they might use to secure material for a paper to read 
at a teachers' association or to arouse the interest of their 
pupils. Such teachers have expressed their approval of the 
tests when their pupils' scores were high, and have consid- 
ered the tests unsatisfactory when the scores were low. 

In order to prescribe the best corrective instruction the 
teacher needs to have as much information as possible. 
Hence, the need for diagnostic tests and for examining the 
test papers to learn of the pupils' errors. Diagnosis requires 
time, but it is justified by making possible the planning of 
more effective corrective instruction. 



APPENDIX 

A sample package of tests. It will be helpful to a teacher 
in reading this book to have at hand sample copies of the tests 
described in it. In a few cases it is almost necessary to have a copy 
of the test in order to understand the discussion of its use. Believ- 
ing that teachers would appreciate the opportunity of being able 
to secure all of the tests from one address, the author has assembled 
packages containing one copy of the tests marked with a star below. 
The other tests have been either reproduced in the pages of this 
book or described so fully that a copy is not needed in order to 
understand the test. A sample package will be sent postpaid upon 
receipt of a post-office money order or a check for 40 cents. Do 
not send stamps. Coins may be sent at sender's risk. Address 
Walter S. Monroe, Bureau of Cooperative Research, Indiana Uni- 
versity, Bloomington, Indiana. 

Ordering tests for class use. All of the tests listed in the 
following table can be obtained from the various publishers. A 
large number of them can be obtained from the distributing cen- 
ters listed below. In ordering from one of these centers there is 
the advantage of being able to secure all, or at least several, of 
the tests desired from one address. In addition these Bureaus are 
prepared to render other important service. Hence, it is recom- 
mended that teachers send their orders to the Bureau of the State 
in which they reside. If their State has no Bureau, they may send 
their orders to the nearest one. The prices of the tests when or- 
dered from a Bureau are generally the same as when ordered from 
the publisher. 

Distributing Centers 

Bureau of Educational Research, University of Illinois, Urbana, 
HI. 

Bureau of Cooperative Research, University of Indiana, Bloom- 
ington, Indiana. 

Educational Extension Service, University of Iowa, Iowa City, 
Iowa. 



286 APPENDIX 

Bureau of Educational Measurements and Standards, Kansas 
State Normal School, Emporia, Kansas. 

Bureau of Cooperative Research, University of Minnesota, 
Minneapolis, Minnesota. 

In the table below detailed information about the tests described 
in the preceding chapters is given. One not familiar with ordering 
tests should study this table carefully in order to be able to ask for 
just what is needed. In some cases the necessary directions and 
record sheets are furnished by the publisher, but this is not true 
in all cases. When it is not done, the one ordering must ask for 
the number of these accessories desired. 

Very important. In ordering tests of which one copy is needed 
for each pupil always give the number of pupils in each grade. This 
is important because some of the series have different tests for the 
different grades. 

Prices. The prices given below are subject to change. In some 
cases the amount of postage is given. In practically all other cases 
the purchaser is charged with the postage but the author does not 
have information in regard to the amount. 



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INDEX 



Adams, John, 170. 

Analytical diagnosis in arithmetic, 
138. 

Arithmetic: Courtis Standard Re- 
search Tests, Series B, 97 ff., 119 
ff.; Monroe's Diagnostic Tests, 
109, 131 ff.; Cleveland Survey 
Tests, 151 ; Monroe's Standardized 
Reasoning Tests, 154 ff.; Stone's 
Reasoning Test, 173; Starch's 
Arithmetical Scale A, 174. 

Arithmetic, types of examples, 111, 
115. 

Arithmetic, vocabulary in, 163, 165. 

Ashbaugh, E. J., 129, 221. 

Ayres, L. P., 176, 178, 208, 221. 

Ayres's Handwriting Scale, " Gettys- 
burg Edition," 207, 209 ff.; Ayres's 
Handwriting Scale, "Three-Slant 
Edition," 208. 

Ayres's Measuring Scale for Ability 
in Spelling, 175 ff., 187-89. 

Bagley, W. C, 262. 
Ballou, F. W., 130. 
Bell and McCollum History Test, 

266. 
Boston Copying Test, 249. 
Boston Geography Tests, 264. 
Branom and Reavis Completion 

Test for Geography, 265. 
Breed, F. S., 209, 244. 
Breed and Frostic Composition Scale, 

244. 
Brownell, Baker, 253. 
Buckingham, B. R., 10, 256. 
Buckingham's Geography Test, 265. 
Buckingham's History Test, 205. 



Charters, W. W., 230, 254. 

Charters's Diagnostic Test in Lan- 
guage and Grammar, 245 ff. 

Chase, Sara E., 165. 

Cleveland Survey Tests, 151. 

Comin, Robert, 11. 

Composition: Willing's Scale for 
Measuring Written Composition, 
235 ff.; Nassau County Supple- 
ment, 243; Hillegas Composition 
Scale, 244; Thorndike Extension 
of the Hillegas Scale, 244; Harvard- 
Newton Composition Scale, 244; 
Breed and Frostic Composition 
Scale, 244. 

Corrective instruction: in reading, 
58 ff., 65 ff., 72 ff., 85, 86 ff.; in 
arithmetic, 121, 123, 124, 128, 131, 
135, 139 ff., 145 ff., 158-60, 168, 
173; in spelling, 192 ff.; in hand- 
writing, 224 ff., 228, 231 ff. 

Counts, George S., 144. 

Courtis, S. A., 107, 111, 138 ff., 182, 
193. 

Courtis's Silent Reading Test No. 2, 
29 ff., 46 ff., 82 ff. 

Courtis's Standard Practice Tests, 
136. 

Courtis's Standard Research Tests, 
Series B, 97 ff.; limitations of, 114. 

Courtis's Standard Tests in Geog- 
raphy, 256 ff. 

Diagnosis: in arithmetic, 119, 122, 
123, 124 ff., 128 ff., 138 ff., 157 ff., 
160 ff., 168 ff.; in reading, 53 ff., 65, 
69 ff., 82 ff.; in spelling, 190 ff.; in 
handwriting, 212 ff., 231 ff.; in 



296 



INDEX 



language and grammar, 245; in 
history, 264. 

Educational measurements, value of, 

267 ff. 
Elliott, E. C, 8. 
Errors in arithmetic, 142 ff. 
Errors in spelling, 194 ff. 

Fordyce, Charles, 182. 

Freeman, F. N., 198, 199, 212, 214, 

215, 233. 
Freeman's Handwriting Scale, 212. 
Frostic, F. W., 244. 

Geography: Courtis's Standard Tests 
in Geography, 256 ff.; Hahn- 
Lackey Geography Scale, 258 ff.; 
Boston Geography Tests, 264; 

: Buckingham's Geography Test, 
265; Starch's Geography Tests, 
Series A, 265; Witham's Standard 
Geography Tests, 265; Branom 
and Reavis Completion Test for 
Geography, 265. 

Gist, Arthur S., 142. 

Gray, C. T., 216. 

Gray, W. S., 67. 

Gray's Oral Reading Test, 39 ff. 

Gray's Score Card for Handwriting. 
216 ff. 

Gray's Silent Reading Tests, 67. 

Haggerty, M. E., 49. 

Hahn, H. H., 258. 

Hahn-Lackey Geography Scale, 
258 ff. 

Handwriting : Ayres's Scale, "Gettys- 
burg Edition," 208 ff.; Freeman's 
Scale, 212; Gray's Score Card, 
216 ff.; measurement of rate, 
203 ff., measurement of quality, 
207; standards, 219 ff. 

Harlan's Test of Information in 
American History, 262 ff. 



Harvard-Newton Composition Scale, 
244. 

Hillegas Composition Scale, 244. 

History: Harlan's Test of Informa- 
tion in American History, 262 ff.; 
Buckingham's History Test, 265; 
Bell and McCollum History Test, 
266; Starch's American History 
Tests, Series A, 266. 

Hollingworth, Leta S., 196, 197. 

Johnson, F. W., 4. 

Jones, N. F., 176, 192. 

Judd, C. H., 67, 73, 76, 84, 225. 

Kallom, Arthur W., 109, 144, 197. 
Kelly, F. J., 3, 9, 278. 
King, W. 1., 105. 
Koos, L. V., 222. 

Lackey, E. H., 258. 

Language and Grammar: Charters's 
Diagnostic Test in Language and 
Grammar, 245; Starch's Punctua- 
tion Scale, 248-49; Boston Copy- 
ing Test, 249. 

Lewis, E. E., 223. 

Lull, H. G., 201. 

Median, calculation of, 29, 35, 102 ff. 

Monroe, Walter S., 109. 

Monroe's Diagnostic Tests, 109. 

Monroe's Standardized Reasoning 
Tests, 154 ff. 

Monroe's Standardized Silent Read- 
ing Tests, 22 ff., 43 ff., 51 ff. 

Monroe's Timed-Sentence Spelling 
Test, 185, 189. 

Nassau County Supplement, 243. 
Nutt, H. W., 225. 

Otis, A. S., 180, 181. 

Race, Henrietta V., 49. 



INDEX 



297 



Reading: Monroe's Standardized Si- 
lent Reading Tests, 22 ff.; Cour- 
tis's Silent Reading Test No. 2, 
29 ff.; Thorndike's Visual Vocabu- 
lary Scale, 36 ff., 49; Gray's Oral 
Reading Test, 39 ff ., 49-51 ; Thorn- 
dike's Scale, Alpha 2, for the un- 
derstanding of sentences, 54. 

Reavis, C. W., 233. 

Rugg, H. 0., 262. 

Rural Schools, use of test in, 25, 32, 
88 ff., 91, 99-100, 137. 

Scores, good arrangement of, 26. 

Sears, J. B., 194. 

Smith, James H., 151. 

Spelling : Ayres's Measuring Scale for 
Ability in Spelling, 176 ff.; Mon- 
roe's Timed-Sentence Spelling 
Test, 185 ff. 

Spelling demons, 192. 

Spelling games, 193. 

Standards: Monroe's Standardized 
Silent Reading Tests, 44; Courtis's 
Silent Reading Test No. 2, 46; 
Thorndike's Visual Vocabulary 
Scale, 49; Gray's Oral Reading 
Test, 51; Courtis's Standard Re- 
search Tests, Series B, 108; Mon- 
roe's Diagnostic Tests, 116; Mon- 
roe's Standardized Reasoning 
Tests, 157; Ayres's Measuring 
Scale for Ability in Spelling, 175 ff., 
187-89; Monroe's Timed-Sentence 
Spelling Test, 185, 189; Handwrit- 
ing, 219 ff., 231 ; WUling's Scale for 
Measuring Written Composition, 
243; Starch's Punctuation Scale, 
249; Boston Copying Test, 252; 
Charters's Diagnostic Test in 
Language and Grammar, 248; 
Hahn-Lackey Geography Scale, 



261 ; Harlan's Test of Information 
in American History, 263. 

Standards, necessity of, 18. 

Starch, Daniel, 8, 9, 174, 181, 248. 

Starch's American History Tests, 
Series A, 266. 

Starch's Geography Tests, Series A, 
265. 

Starch's Punctuation Scale, 248-49. 

Stone, C. R., 230. 

Stone, C. W., 109, 159, 173. 

Studebaker's Economy Practice Ex- 
ercises, 136. 

Terman, L. M., 71. 

Thorndike, E. L., 54, 56, 57, 105. 180, 

181. 
Thorndike's Extension of the Hille- 

gas Composition Scale, 244. 
Thorndike's Handwriting Scale, 208. 
Thorndike's Scale, Alpha 2, for the 

Understanding of Sentences, 54. 
Thorndike's Visual Vocabulary Scale, 

36 ff. 

Uhl, W. L., 92, 149. 

Vocabulary: Thorndike's Visual Vo- 
cabulary Scale, 36 ff. 
Vocabulary in arithmetic, 163, 165. 

Wasson, Alfred W., 94. 

Willing, M. H., 235. 

Willing's Scale for Measuring Writ- 
ten Composition, 235 ff. 

Wilson, H. B., 229. 

Wilson, G. M., 229. 

Witham's Standard Geography 
Tests, 265. 

Yawberg, A. G., 269. 

Zirbes, Laura, 79, 86 ff., 91. 



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